You want the long or short answer? Because the short answer is "No."
As you look at worldwide data for things like fertility rates and infant mortality, you find that in first world countries women generally have few children and those children are unlikely to die in their infancy. You could argue that a mother in the US or Europe has no need to give birth every few years in order to have a child that survives long enough so that they too can have children.
But if you look at third world countries, women are having 4, 5, 6 children over the course of their lives, with infant mortality rates at 1 in 10. Again, it could be argued that mothers are having more and more children in an attempt for some of them to survive past infancy.
But it's not just infant mortality that is the problem for the third world, general health is poor - surviving into your teens does not mean surviving into your twenties. While the west is content with small families, the third world isn't, and this is just one angle that we could talk about.
What Bill Gates refers to is that with better healthcare worldwide, there will be less need for a higher population if that makes sense.
If you haven't already seen the 30 minute talk from Bill to get the context of what he's saying, I suggest you do, as well as TED Talks from Hans Rosling, whose site Gapminder gives you huge amounts of data sets to look through and combine on all manner of issues effecting the world.