For a few generations. Eventually, the survival of the fittest kicks in, and those people who avoided birth control (from a stronger paternal feeling, etc) will restock the population.
This sounds like the same fallacy that the movie Idiocracy is based on – even if you pass on your genes, that doesn't mean you pass on traits like demographic fertility, or intelligence.
One of the best predictors of a woman's fertility rate is their level of education. Higher education leads to fewer children on average. This is largely independent of the fertility of their parents.
Also, if you look at the third world, there are actually some good economic arguments for having more children, related to infant mortality. Your children are your 'Social Security', so you want to ensure that some survive. Paradoxically, reducing infant mortality can actually reduce fertility. http://video.google.com/videoplay?docid=-5192204318056302269
And additionally, humans have a vast ideological landscape that is "contagious" among individuals, which also happens to limit breeding. This is not something evolution can control through reasonable means.
