Once in the air when it's almost certainly going to take more than 15 minutes (and thus the damage, if there is damage, is done, to get the idiot off the aircraft, there is little reason for the Captain to turn the flight around although it's the Captain's discretion.
What does seem to be clear on AA, as well as at least the other legacies is that once booted, one is banned as well. The only carrier for which I've seen transparent reporting is DL. It had banned 240 people as of about 2 weeks ago.