Yeah, that's correct and a very sensible way of getting the most out of your chiller.

I wouldn't recommend trying to air cool the hotside. The reasons I'm air cooling my hot side is:

Lower cost,
lower noise (that's not likely but still possible),
smaller size,
to be different,
to prove that it can be done,
because my heatload is spread over a large area,
and because I don't think it will be much worse than water cooling if done carefully.