Who has more power? Air Force One PIC or ICAO or FAA?
First, ICAO has no authority over aircraft movement in and of itself. It's a United Nations agency that, as Wikipedia puts it "codifies the principles and techniques of international air navigation and fosters the planning and development of international air transport to ensure safe and orderly growth." Individual sovereign nations accept whatever they want of what ICAO codifies, and it is the governing aviation authority of the individual nation that has the power.

Now, in the U.S., military aviation is not governed by the FAA, the civilian agency that for the most part complies with ICAO recommendations as do most countries. However, the U.S, government has a common air traffic control system for both military and civilian aircraft. If, for no good reason, an aircraft violates the air traffic rules, the FAA will deal with that for civilian aircraft, the military for military aircraft.

Air Force One is a military aircraft. Further, as @Zach Lipton has pointed out, it is a "state aircraft." Further, whichever airplane is carrying the President of the United States is designated Air Force One (or Marine One or Navy One) only when carrying the President, and the President is the Commander-in Chief of the military. I don't know how all that sorts out, but practical considerations dictate a general adherence to the "rules of the road" so to speak.

And finally, it's accepted practice that the captain of an aircraft is the final authority aboard the aircraft for the operation of the aircraft, regardless of who is aboard.

Better to rule by consensus than by diktat if there's time for consensus.