Easily. Thousands died in the early years from illegal abortions. And even if the number of dead women declined somewhat, the amount of harm done is still best described as very high. That the number of deaths declined is mostly due to doctors performing either the procedures or treating the resulting health consequences. It's just that the officially registered deaths from illegal abortions immediately before Roe vs Wade were a little lower than "thousands".
It also ashould be noted that while Roe was a landmark case, it is a stand-in for "less extreme anti-abortion laws", and those started to change slightly earlier.
But there are several factors to observe when analysing the timeline. Given the size of the population, the unspecified time-span and the mere numerical "thousands":
By the end of the decade of the 1870s, medical writers began to suggest earlier estimates had been, if anything, too low. In 1878 physicians testifying in the closely watched murder trial of an abortionist in southern Illinois set the ratio at 25 percent of all pregnancies.89 In Wisconsin the situation seemed even worse. According to the state medical society's report to AMA headquarters in 1879, "where one living child is born into the world, two are done away with by means of criminal abortion."90 The Wisconsin report was greater by a factor of two than any other medical estimate of the period, and can probably be discounted. But less easily dismissed was still another upward revision of the Storer and Heard ratio of one abortion in every five pregnancies made by the Michigan State Board of Health two years later.
Physicians in Michigan, according to a special committee of the Board of Health, were directly aware of "seventeen abortions to every hundred pregnancies," and were also convinced that at least "as many more… never come to the physician's knowledge, making 34 percent, or one-third of all [pregnancies] ending in [purposeful] miscarriage." The Michigan report calculated that "not less than one hundred thousand" abortions were performed each year in the United States and "not less than six thousand" women died annually from the immediate effects of an abortion. The committee's data, like that in Philadelphia, had been collected by mail; one member of the committee had gathered responses from nearly a hundred doctors around the state.
Occasionally during the 1880s a physician might estimate an abortion rate as low as "ten percent of all pregnancies," but most writers arrived at calculations at least as high as the Michigan rate of one-third.93 A doctor who had practiced in Philadelphia for twenty-five years "stated as his firm conviction that more than one-half of the human family dies before it is born, and that probably three-fourths of the premature deaths are the direct or indirect result of abortion by intent." (p81–82)
–– James C Mohr: "Abortion in America The Origins and Evolution of National Policy/ 1800–1900", Oxford University Press: Oxford, New York, 1978.
That is in the 19th century with lower population numbers.
If we look more closely in time to Roe vs Wade in 1972, then we get
A 1951 Ebony article on “the abortion menace,” for example, included a series of photos depicting a woman meeting an unknown connection on a dark Corner, the abortion procedure being performed in an apartment, and, finally, several police officers Standing in a circle around a bed and pulling a sheet over a dead woman’s body.
The headline announced that abortion “claims 8,000 lives of desperate mothers-to-be” every year, including “several thousand Negro women.”96 A decade later, a three-part investigative series on abortion in the mainstream Saturday Evening Post followed the same pattern. Headlines declared that “every day thousands of American women risk their lives” by having abortions. Ebony depicted the death and victimization of an African American woman; photos in the Saturday Evening Post featured young white women who had died. Both included photos of the abortionist’s equipment and guilty abortionists.97 Avid readers learned that abortion was deviant, dirty, and dangerous; those who might know otherwise endured shame and secrecy.
–– Leslie J Reagan: "Dangerous Pregnancies: Mothers, Disabilities, and Abortion in Modern America", University of California Press: 2010.
The whole thing was illegal, which means that exact numbers are not available in the statistics. These very conservative estimates and eventually scarcely available numbers underreport systematically the real numbers, but still:
Mortality From Induced Abortionbefore 1973
It is impossible to know for certain how many induced abortions took place before 1969, the year the CDC began its surveillance of the number of abortions and abortion deaths in the United States. Tietze28 estimated that prior to the adoption of more moderate abortion laws in 1967, there were 1 million abortions annually nationwide, of which 8000 were legal, resulting in an abortion rate of five per 1000 people and an abortion ratio of 30 per 100 live births.
The only available national data on abortion-related deaths prior to 1969 come from death certificate information reported to the vital statistics system of the National Center for Health Statistics (NCHS) (Hyattsville, Md). The NCHS estimates of abortion-related deaths are considered conservative because many deaths that were abortion-related were not listed as such on the death certificate. The physician may not have known that the death was abortion-related or may have omitted that information on the death certificate, given the stigma and illegality associated with the procedure.29 However, NCHS data offer the only information on abortion-related deaths before 1969 that allow comparisons to be made overtime.
Legal and Illegal Abortion-Related Deaths per Million Women Aged 15 to 44 Years, United States, 1958 Through 1972
–– Yank D. Coble Jr, MD; E. Harvey Estes Jr, MD; C. Alvin Head, MD; et al; Council on Scientific Affairs, American Medical Association: "Induced Termnation of Pregnancy Before and After Roe v Wade. Trends in the Mortality and Morbidity of Women", JAMA. 1992;268(22):3231-3239. doi:10.1001/jama.1992.03490220075032
Perhaps relevant: after an illegal abortion developed complications that may result in death, there were still medical treatment options, which if omitted would have increased the death toll astronomically. The death rate was only so low in the late 20th century because all those women that were harmed grievously were eventually treated properly:
In more accessible language:
Illegal Abortions Were Common
Estimates of the number of illegal abortions in the 1950s and 1960s ranged from 200,000 to 1.2 million per year. One analysis, extrapolating from data from North Carolina, concluded that an estimated 829,000 illegal or self-induced abortions occurred in 1967.
One stark indication of the prevalence of illegal abortion was the death toll. In 1930, abortion was listed as the official cause of death for almost 2,700 women—nearly one-fifth (18%) of maternal deaths recorded in that year. The death toll had declined to just under 1,700 by 1940, and to just over 300 by 1950 (most likely because of the introduction of antibiotics in the 1940s, which permitted more effective treatment of the infections that frequently developed after illegal abortion). By 1965, the number of deaths due to illegal abortion had fallen to just under 200, but illegal abortion still accounted for 17% of all deaths attributed to pregnancy and childbirth that year. And these are just the number that were officially reported; the actual number was likely much higher.
Poor women and their families were disproportionately impacted. A study of low-income women in New York City in the 1960s found that almost one in 10 (8%) had ever attempted to terminate a pregnancy by illegal abortion; almost four in 10 (38%) said that a friend, relative or acquaintance had attempted to obtain an abortion. Of the low-income women in that study who said they had had an abortion, eight in 10 (77%) said that they had attempted a self-induced procedure, with only 2% saying that a physician had been involved in any way.
These women paid a steep price for illegal procedures. In 1962 alone, nearly 1,600 women were admitted to Harlem Hospital Center in New York City for incomplete abortions, which was one abortion-related hospital admission for every 42 deliveries at that hospital that year. In 1968, the University of Southern California Los Angeles County Medical Center, another large public facility serving primarily indigent patients, admitted 701 women with septic abortions, one admission for every 14 deliveries.
A clear racial disparity is evident in the data of mortality because of illegal abortion: In New York City in the early 1960s, one in four childbirth-related deaths among white women was due to abortion; in comparison, abortion accounted for one in two childbirth-related deaths among nonwhite and Puerto Rican women.
Even in the early 1970s, when abortion was legal in some states, a legal abortion was simply out of reach for many. Minority women suffered the most: The Centers for Disease Control and Prevention estimates that in 1972 alone, 130,000 women obtained illegal or self-induced procedures, 39 of whom died. Furthermore, from 1972 to 1974, the mortality rate due to illegal abortion for nonwhite women was 12 times that for white women.
–– Rachel Benson Gold: "Lessons from Before Roe: Will Past be Prologue?", Guttmacher Policy Review, Volume 6, Issue 1, 2003.
In the decade when Grimes was born, the 1940s, there were records of more than 1,000 women dying each year from unsafe and largely self-induced abortions. Every large municipal hospital in the U.S. had a “septic abortion ward,” and treatment for the complications from so-called “incomplete abortion” was the single leading cause for admission for OB-GYN services across the country. National Opinion Research Center surveys conducted in the 1960s found that hundreds of women were attempting to self-abort by penetrating themselves with knitting needles, coat hangers, bicycle spokes, ballpoint pens; others tried to swallow chemicals like turpentine, laundry bleach, and acid.
“When the laws began to change, almost overnight, deaths from septic abortion disappeared,” he told ThinkProgress. “Any way you look at it, abortion has been an astounding public health success.”
–– Interview of David Grimes by Tara Culp-Ressler: "What Americans Have Forgotten About The Era Before Roe v. Wade", Think Progress, NOV 19, 2014,
The connection in all this is quite simple:
When conducted in a legal setting and under safe conditions, abortion is an extremely effective and safe procedure. Tragically, almost half of all abortions that take place in the world are conducted under unsafe conditions, mostly in countries where abortion is illegal or highly restricted. These unsafe abortions are a major cause of maternal death and disability. Restricting a woman’s access to abortion does not prevent abortion but simply leads to more unsafe abortions. Barriers to safe abortion are many but include legal barriers, health policy barriers, shortages of trained healthcare workers, and stigma surrounding abortion.[…]
When conducted in a legal setting and under safe conditions, abortion is an extremely safe procedure associated with few complications. US data suggest that it is as safe as or safer than most common outpatient medical procedures and safer than childbirth.[…]
Yet almost half of the 55.7 million abortions that are estimated to take place each year in the world (an estimated 25.1 million abortions) are considered unsafe (17.1 million less safe plus 8.0 million least safe) 6. The WHO defines unsafe abortion as a procedure for terminating a pregnancy by persons who are not appropriately trained or use a non-recommended method (less safe) or both (least safe) 6. Unsafe abortions lead to a high burden of complications, maternal deaths, and costs. Recent estimates for the global distribution of safe, less-safe, and least-safe abortions show that when the legal status of abortion is considered, the proportion of least-safe abortions is greatest in countries with highly restrictive abortion laws, most of which are developing countries.
–– Sharon Cameron: "Recent advances in improving the effectiveness and reducing the complications of abortion", F1000 Research, Version 1, 7, Rev-1881, 2018, doi: 10.12688/f1000research.15441.1
Summary
If one wants to be a math-minded stickler who is taking every word at face-value:
then no, in 1972 there is no official record of reliable and exact statistics of more than one thousand (>1000) women dying from the effects of illegal abortions.
But this is an interpretative act by that stickler, reading an illusory precision into a statement that is imprecise. Since this claim is political and as such a communication enabling shorthand ("thousands" usually isn't used mathematically but colloquially) for "many women died needlessly, when proper procedures were available, just because of this prohibition, before this prohibition was overturned", then the claim is perhaps slightly exaggerated for the last few years before 1973 but acceptable in its general direction.
Abortions will take place, and if they are illegalised, and thus made unsafe, many more women will die, as this is what happened when the legal situation was "prohobition".