I'm in the home stretch of a Domination Victory, and I can report that the AI is certainly building planes, but its use of them is a little sketchy.
I invaded Macedon and he managed to strafe me with his Fighters a couple of times (pretty effective since my Infantry had no air support). But at one point before I was taking his capital, Alex just shuffled his Fighters uselessly between cities instead of actually attacking my units (which would have been pretty nasty since I didn't have AA yet). I did see Alex use a Bomber to take Auckland a few turns later.
After Alex was done, I launched a fleet over to invade Pedro. He had a Biplane in his city too but didn't use it. At this point I had some AA units with me, so maybe that put him off, but I wouldn't count on it.
It seems there is some improvement, but as with land units, the AI has issues with target prioritisation and movement.