I'm not sure that's true. By the same argument, you might say that free vaccines would encourage overpopulation, but (according to Bill Gates at least) the data shows the opposite:

"In society after society, he saw, when the mortality rate falls—specifically, below 10 deaths per 1,000 people—the birth rate follows, and population growth stabilizes." (http://www.forbes.com/sites/matthewherper/2011/11/02/the-sec...)