I don't THINK there's harm in the air. I know for some chemical treatments it's suggested to run additional air into the water because of the treatments.
There is also a long running debate on if "air injection treatment" of nano bubbles into a tank is a good thing or not. There are several threads on here about it. Essentially turns your display into one giant skimmer temporarily.
Fish, corals, algae, inverts, and everything else need air to survive.
I think it MAY affect some fish that have swim bladders, but I am in no way certain. I would do more research.