No. It'll just get whatever co2 that's built up in the head space into solution. Make sure you've given the bottles enough time to carb & condition at room temp before fridge time. usually 3-4 weeks for the average gravity ale.
The assumption here is that you're botteling. If you're kegging and force carbonating, it will carbonate just fine in the fridge. Botteling and using the left-over yeast to carbonate - definitely do it at room temperature to keep the yeast active.