Last October in Austin, there was a bitter irony: after heavy rains, the systems for filtering the water were overloaded and they put out a warning that water wasn't safe to drink (though fine for other purposes).
"Water, water, everywhere, but not a drop to drink."
In many areas, not appreciably. Aquifer contraction and all the pavement lain in the past century end up blocking a lot of absorption. A recent 99% Invisible episode talked about this, focusing on Mexico City's aquifer situation:
https://99percentinvisible.org/episode/depave-paradise/
No, floods just wash by, eroding top soil and often decreasing future aquifer replenishment because there is less to hold on to the water to give it time to soak down into the aquifer.
"Water, water, everywhere, but not a drop to drink."
Story about it:
https://patch.com/texas/downtownaustin/austin-water-safe-dri...