Yes, they do, but if what goes in is insufficient by a wide margin, people who can afford to will start drilling for water.

Assuming that the water taken through qanats would eventually make it into aquifers (fat from unlikely, I think, as it takes water from underground that’s less likely to evaporate) one could even argue that tapping rainwater with qanats prevent aquifers from getting refilled, so it’s taking from the same water source.