I recently read Dan Brown's Inferno - not a great reference work by any stretch, but some compelling arguments are made along the lines you suggest.

I suspect there is a lot more to it than just limiting the numbers of babies born. If there are more resources per person (a consequence of fewer people) then we will likely see the resources used per person go up.

Anecdotally - American cars are terribly inefficient with respect to fuel consumption. This is I think partly due to the low cost of fuel. In the UK, however, the cost of fuel per litre is almost double that of the US, and consequently people gravitate toward much more efficient vehicles.

Additionally - China has been a huge polluter for quite some time despite one child policies though admittedly it's partly because the global economy outsourced their pollution to China to a degree.