No.
The 'eat your vegs' campaign as an established social norm is older, started with World War One, not during the Depression. Further, spinach is no meat substitute, whether you look for any iron or protein. Whether 'the government' provided some funds as well to this is possible, but for example the "Commonwealth Fund is a private U.S. foundation".
Indirectly, this campaign against malnutrition also involved many politicians and a few agencies, like the USDA and US Children's Bureau. But such early efforts meant that there was no need to directly influence a cartoon, which merely drew upon existing stereotypes. That an already hugely popular comic would need such an 'incentive' seems highly questionable.
What Popeye allegedly achieved was indeed a certain demand from children for spinach, primarily fresh, but also the canned and thus unsavory Popeye form, protecting American farmers somewhat from the effects of depression. But by that time consumption of greens in general went up steadily to an all-time high in 1945. Despite the processing – not least into cans – destroying a good part of the then en vogue vitamins, which were sometimes re-introduced as 'fortifications' or then sold as popular pills. Spinach sales went up, and so did other leafy vegetables and foods independent of season or region in general.
— Harvey Levenstein: "Paradox of Plenty. A Social History of Eating in Modern America", Oxford University Press: Oxford, New York, 1993. / Harvey Levenstein: "Fear of Food. A History of Why We Worry about What We Eat", University of Chicago Press: Chicago and London, 2012.
That Popeye was then used later as a role-model for
to be known as entertainment-education:
the process of purposively designing and implementing a mediating communication form with the potential of entertaining and educating people, in order to enhance and facilitate different stages of pro-social (behaviour) change” (Bouman, 1999: 25).
— Thomas Tufte: "Entertainment-education in development communication. Between marketing behaviours and empowering people", in: "Media and Glocal Change: Rethinking Communication for Development", CLACSO, Consejo Latinoamericano de Ciencias Sociales, Buenos Aires, 2005 (PDF)
does not mean that he was designed as one in the first place.
Hamblin was wrong. In reality, Popeye’s creator EC Segar never once
had his superhero eat spinach for iron. In 1932, in the only cartoon by Segar where Popeye explains exactly why he eats the stuff, the cartoon sailor with the bulging forearms claims in in his garbled English:
Spinach is full of Vitamin A. An'tha's what makes hoomans strong and helty.
In fact, spinach contains beta-carotene, which is converted to vitamin A in the human body. And Popeye is as right today with his dietary advice as he was in the last century, eating spinach is a good way to get Vitamin A.
The scandal of the Spinach Supermyth is not the decimal error myth started by Bender and spread by Hamblin. Rather, it is that people continue to make poor dietary choices based on the belief that spinach is a good source of iron. If only we could discover what the interactive ingredients and contexts are for the enduring success of the Spinach, Popeye and Iron Decimal Point Error Myth, we could reverse engineer the myth and seek to apply the lessons learned from that with an aim to entrench veracious knowledge about nutrition and other information.
— Mike Sutton (1): "How the spinach, Popeye and iron decimal point error myth was finally bust", HealthWatch Newsletter 2016;101:7 (PDF)
For an even more entertaining version of the above, and a proper SkepticsSE recommended reading on proper research and referencing of facts and findings:
At least since 1981, literally hundreds of expert scholars in various diverse fields have published materials that treat the SPIDES as unquestionable and yet have apparently not fact checked the actual origin of the story, because they provide no references to support it.
— Mike Sutton (2): "Spinach, Iron nd Popeye: Ironic lessons from biochemistry and history on the importance of healthy eating, healthy scepticism and adequate citation", Internet Journal of Criminology, 2010. (PDF) The 'wrong being Hamblin' responds to the iron myth himself here.
And for the timeline:
Popeye ate spinach because the association of spinach with strength was a product of the first national nutrition crisis in the United States: the 1920s fight against child malnutrition.
Educators and public health experts sponsored by the Com- monwealth Fund modeled their efforts on propaganda campaigns aimed at instilling nutritional norms by convincing children that everyone was eating spinach, drinking milk, and brushing their teeth. Indeed one of the lasting effects of this nutrition crisis was the construction of social norms regarding health and nutrition embodied in popular admonitions such as “Eat your vegetables” or “Don’t drink coffee; it will stunt your growth.”
From his first films in 1933, Popeye the Sailor relied on spinach to allow him to settle scores (Grandinetti 2004). Indeed, for decades, the feisty sailor’s reliance upon canned spinach was credited with increasing its consumption by a third during the Great Depression, making it at the time the third favorite food among children, after turkey and ice cream (Oxford Encyclopedia 2004). Popeye’s producers at Fleischer Studios did not invent the association between spinach and strength; they exploited a social norm instilled in the course of the malnutrition crisis.
Programs such as the Commonwealth Fund’s had succeeded in changing social norms regarding nutrition. By the time that the first celluloid representation of Popeye would reach for his trusty spinach in the 1930s, the cartoonists could draw upon a shared understanding of nutrition and vitamins among American children.
— Laura Lovett: "The Popeye Principle: Selling Child Health in the First Nutrition Crisis", Journal of Health Politics, Policy and Law, Vol. 30, No. 5, October 2005. (PDF)
Therefore:
The fact that spinach consumption was on a steep upward trend between 1915 and 1928 makes all the more pertinent my Question 4 regarding the need for evidence that Popeye alone was responsible for a 33 percent increase in spinach consumption; particularly since Popeye never ate spinach until June of 1931 (See: Segar 2007 p 40). Was canned spinach perhaps promoted for its iron content at any time before or after Popeye started advocating it?
Incidentally, in the earlier newsprint cartoons, Popeye displays superhuman characteristics without recourse to any nutritional assistance. Popeye survives several bullet wounds on May 16th 1929 by stroking the three hairs on the head of Bernice the good luck whiffle hen. Later, in October 1930, Popeye relies solely upon a meal of beef to overcome mere bedridden weakness from a total of 25 bullet wounds. It was around this time, though a little earlier, on July 22nd 1929, that spinach first makes an entry into the Popeye comic strip, not as a foodstuff but as Miss Spinach, the landlady of the cad Mr Herringbone. All of these minor historical details aside, after that beef meal in 1930, Segar settled on spinach for Popeye in 1931 and his comic creation remained faithful to eating and promoting it thereafter.
The fact that Popeye was already doing his tough guy stuff well before he became a spinach user suggests that Segar may well have later made a decision to employ his creative work to support programmes promoting spinach consumption during the US nutritional crisis. I am not sure, therefore, how exactly it is possible to isolate the influence of Segar’s Popeye from that of wider nutrition programmes on spinach consumption.
(Sutton-2)
But a caveat is still needed. The above is by no means the counter fact to provide a narrative that attempts to show a more a less uniform campaign for greens in the US at the time. The field of nutrition was and is always full of contradicting information, and always full of extremists' advice and proscriptive content informed by ideology. Well into the age of Popeye beef and milk were primary targets to promote, with often questionable logic on 'protein' and then 'vitamin A' (yes, just like in spinach, but the more vitamins were discovered the more any one food could advertise that it had 'it/them'), and sometimes with a good measure of added racism mixed in:
Therefore, the industry’s economic interests played into the racial rhetoric of the day, which portrayed Asians as effeminate and enfeebled and the Chinese “leaf diet” as a cause of degeneracy. Gastropolitical racial exclusions and the politics of health and nutrition were closely linked in the congruence of the ideal American body politic and the ideal American body. It would be many decades before nutritionists began to publicize the benefits of leafy greens such as spinach, which even then could be touted only because a cartoon sailor, Popeye, ate it in a very safe, very American form: boiled and from a tin can.
— E. Melanie du Puis: "Angels and Vegetables A Brief History of Food Advice in America", Gastronomica: The Journal of Food and Culture, vol.7, no.2, pp.34–44, 2007. (PDF)
looking for ways to promote iron-rich spinach" - oh, the iron-y