Yes, but that does not mean it is now clean water. Anything could happen between the moment Google ingests it and spits it back out, the assumption that it is 'just' a little warmer is nice but it misses the option of for instance contamination from a secondary circuit or various substances leaching into the water used as a coolant.

But I mean, the water is not discarded, it is constantly reused. I assume some is lost over time, but surely it is minimal?

So where toes the "not clean water" go then usually in such a setup?

Water treatment plants.