Now this is a very amusing question. That answer is somewhat yes--for adolescents and young adults, that is.
In their latest Institute for the Study of Labor paper entitled, "Does More Money Make You Fat? The Effects of Quasi-Experimental Income Transfers on Adolescent and Young Adult Obesity," Randall Akee, Emilia Simeonova, William Copeland, Adrian Angold and Jane Costello examine how exogenous income transfers during adolescence affect contemporaneous body mass index (BMI) measures and young adult obesity rates using evidence from the Great Smoky Mountains Study of Youth.
Their finding is, it depends on the initial socio-economic status and they also actually find an inverted U-shaped relationship between initial income and BMI:
"Youths who resided in families that had high pre-treatment annual incomes experience no change in young adult obesity rates as a result of the income transfers, while the BMI of poorer children increases. Adolescents coming from worse-off households experience an increase in weight only, without the corresponding change in height."
The thing also is, the effect is continuous as the individual gets older:
"The cumulative effects of the increase in household income persist for several years into young adulthood."
It seems there is no behavioral aspects to their analysis, which should be worth considering. But this surely has serious implications for government policy regarding child obesity. The worst part is, if you believe in this study, you're not going to look at government income transfers to poor households the same way again.