This doesn't seem to track with broader sociological trends. For example, let's compare the USA, one of the most religious Western countries, with the USSR, where 60%+ of the population was atheistic, and where the state promoted atheism. Between 1960 and 1980, the US population grew from 179M to 226M (a 26% increase). The USSR population grew from 208M to 262M (a 25% increase). So, despite massive differences in religiosity, the population rate was pretty similar. China, another largely atheistic state, grew from 582M to 1B in roughly the same period - a 73% increase.

So while it may be true that certain small deeply religious populations are more incentivized to have children, this doesn't seem like a significant effect at population levels overall. You'll also find small non-religious groups with similar behaviors.