Historically large data centers used evaporative cooling. So the water disappeared in sense that it's no longer available in a useful form in it's original locations. That's changing with growing use of closed-loop systems.
A lot of people think it does, surprisingly. People memed too hard about "querying ChatGPT drains lakes" and anyone who contested it was deemed a booster, so it stuck.
It doesn't mean the water goes back into the same sources it was pulled from, though
Water in the atmosphere doesn't help much when the aquifer that is supplying your water effectively runs out. Even if all that evaporated water comes down as rain in the same region, it still takes years to centuries to get to the aquifer.
no it doesn't but it doesn't go back to where it was taken from either. So it does affect local aquifers.