Not necessarily. Demographics indicates that developed nations seem to have near-replacement birth rates. Anything less than 1 and you get exponential decay. So a small nudge will eventually lead to large reductions in population, but the rate of decline need not be severe.

There are of course issues that a lot of the economy is predicated on growth, but again, I'm actually pretty optimistic that markets and humans are pretty resilient and adaptable given enough warning and time.