My answer would be no, but it is not clearly proved nor provable (I don't see how it could ever be proven). I wanted to take a different angle than the other answers and I hope it will help the readers to draw their own conclusions.
If there is a correlation between population control and homosexuality, there should also be a correlation between the homosxuality rate through the ages. Sadly, we were not there to poll the population in ancient times even though it is known that homosexuality was present and accepted in ancient Greece  for instance. However, we do have surveys from the early 50's when the world population was only 2.5 billions compared to today 7 billions. So, looking to the research papers, can we see a correlation?
The surveys in scientific literature
1948  (World pop.: around 2.4 billions)
Had homosexual experience: 37%
More or less homosexual: 10%
Exclusively homosexual: 4%
1974  (World pop.: around 4 billions)
Had homosexual experience: 27%
More or less homosexual: 7%
Exclusively homosexual: 2-3%
1977  (World pop.: around 4.1 billions)
More or less homosexual: 3.1%
Exclusively homosexual: 1.3%
1989  (World pop.: around 5.3 billions)
Had homosexual experience: 20.3%
More or less homosexual: 3.3%
1990 to 1995 [6-12] (World pop.: around 5.3-5.7billions)
Had homosexual experience: 9-20.8%
More or less homosexual: 2-9%
Exclusively homosexual: 1-4%
2002  (World pop.: around 6.5billions)
Bisexual: 1.8% (including bisexual)
Exclusively homosexual: 2.3%
2006-2008  (World pop.: around 6.8billions)
Had homosexual experience: 4-6%
Exclusively homosexual: 2-4%
Considering the scientific surveys, if there is any correlation to make between homosexuality rate and population, it would be that it is decreasing as population grow. However, it is widely accepted that the decrease after early research by Alfred Kinsey is more related to wrong estimates in the first place . Moreover, we can see that the rate vary a lot between different surveys reflecting inherent uncertainty of the sexual orientation.
We could also look into the census done by different countries to see if the densily populated ones show higher homosexuality rate. Warning! depending on the country, the statistics are more or less accurate.
Canada  - Density: 3.41/km^2 - Homosexuality rate: 1.1% - Bisexual: 0.9%
United States  - Density: 34.2/km^2 - LGBT rate: 3.4%
China  - Density: 139.6/km^2 - Homosexuality rate: 0.8-4%
United Kingdom  - Density: 255.6/km^2 - Homosexuality rate: 1.1% - Bisexual: 0.4%
French Republic  - Density: 116/km^2 - Homosexual couples: 0.6% (no data on homosexuality)
Norway  - Density: 255.6/km^2 - Not Hetero: 1.1% - Do not wish to answer: 5.9%
In conclusion, from the statistics, there does not seem to be any link between the popuplation number and density and the homosexuality rate. Therefore, it does seem to contradict the claim that homosexuality exist to control the population growth.
 Davidson, J. (2007). The Greeks and Greek love: a radical reappraisal of homosexuality in Ancient Greece. Weidenfeld & Nicolson.
 Kinsey, A., Pomeroy, W., and Martin, C. (1948). Sexual Behavior in the Human Male. Philadelphia: W.B. Saunders.
 Hunt, M. (1974). Sexual Behavior in the 1970's. New York: Dell.
 Pietropinto, A., and Simenauer, J. (1977). Beyond the Male Myth. New York: Times Books.
 Fay, R., Turner, C., Klassen, A., and Gagnon, J. (January 1989). Prevalence and patterns of same-gender sexual contact among men. Science 243, 338-348.
 Harry, J. (1990). A probability sample of gay males. Journal of Homosexuality 19(1), 89-104.
 Smith, T.W. (1991). Adult sexual behavior in 1989: Number of partners, frequency of intercourse and risk of AIDS. Family Planning Perspectives 23(3), 102-107.
 Janus, S., and Janus, C. (1993). The Janus Report on Sexual Behavior. New York: John Wiley & Sons.
 Billy, J., Tanfer, K., Grady, W., and Klepinger, D. (1993). The sexual behavior of men in the United States. Family Planning Perspectives 25(2), 52-60.
 Taylor, H. (1993). Number of gay men more than four times higher than the 1 percent reported in a recent survey. The Harris Poll #20. New York, NY: Louis Harris & Associates.
 Laumann, E., Gagnon, J.H., Michael, R.T., and Michaels, S. (1994). The Social Organization of Sexuality: Sexual Practices in the United States. Chicago: University of Chicago Press.
 Sell, R. L., Wells, J. A., and Wypij, D. (1995). The prevalence of homosexual behavior and attraction in the United States, the United Kingdom and France: Results of national population-based samples. Archives of Sexual Behavior 24(3), 235-248.
 Mosher WD, Chandra A, Jones J. Sexual behavior and selected health measures: Men and women 15–44 years of age, United States, 2002. Advance data from vital and health statistics; no 362. Hyattsville, MD: National Center for Health Statistics. 2005.
 Chandra A, Mosher WD, Copen C, Sionean C. (2011)Sexual behavior, sexual attraction, and sexual identity in the United States: Data from the 2006–2008 National Survey of Family Growth. National health statistics reports; no 36. Hyattsville, MD: National Center for Health Statistics.
 McWhirter, D., Sanders, S., and Reinisch, J. (Eds.). (1990). Homosexuality/Heterosexuality. The Kinsey Institute Series. New York: Oxford University Press.
 Gates, Gary J.; Newport, Frank (October 18, 2012). "Special Report: 3.4% of U.S. Adults Identify as LGBT".