The USMC can operate from carriers just fine, but where would the USAF operate from? Taiwan? Japan? Diego Garcia?
I don't think the PLA would let us set up on Taiwan, and Japan would throw a fit if we compromised their neutrality. Diego Garcia is too far away for USAF ops in support of the fleet. I think that the USN might be on its own.
I don't know. Japan has a vested interest in keeping the region stable, and Chinese aggression would definitely be a destabalizer. They might allow us to fly from Japan. If not, we at least don't have to fly from Diego Garcia. We can fly from Guam. It's a long way off, probably too far for fighters, but we can still deploy long range strategic bombers there. B-52s shooting anti-ship cruise missiles (and each bomber can carry 8 harpoon anti ship missiles or 20 air-launched cruise missiles, so do that math for a flight of six bombers) from afar and B-2s striking their command and control onshore would be an extremely potent force to augment the USN against Chinese naval and air forces.
Japan could very well join the fray, or at least allow us to operate from there, in the event of PRC aggression against the ROC.
Korea would be an interesting situation and I am almost willing to bet that the North would take advantage of such a situation to try and go south while we were distracted. In fact, a more likely scenario IMHO, would be the N. Koreans going south first, getting us involved over that...and then China making its play for Taiwan.
In either event there is Guam for long rang missions, tanker assisted fighter cover, or long range B1 or B2 missions.