if a batted ball arcs OVER the foul pole when it crosses the fence, is it a home run? Assume the ball crosses directly over it while in flight, not hitting it, but going over.
This would be a home run. The foul pole is simply a vertical extension of the foul line at a point, but the line itself (although it's painted flat) could be abstractedly envisioned to go vertically with no limit. For example, if there is a line drive down the foul line that is caught, you can still distinguish a ball being fair or foul even though it never hit the playing field (or any pole).
From the Official MLB Rules in the Definition of Terms section:
FAIR TERRITORY is that part of the playing field within, and including the first base and third base lines, from home base to the bottom of the playing field fence and perpendicularly upwards. All foul lines are in fair territory.
Importantly, the foul lines are included in fair territory and the perpendicular property is stated.
A FAIR BALL is a batted ball that ...[skip some stuff]... while over fair territory, passes out of the playing field in flight. A fair fly shall be judged according to the relative position of the ball and the foul line, including the foul pole, and not as to whether the fielder is on fair or foul territory at the time he touches the ball.
Note there that the foul pole is included as being part of fair territory, that the relative position of the ball to the foul line is what matters (so it never has to touch anything), and in the case you present of a ball flying over the foul pole--this is the point of the ball passing "out of the playing field in flight"; this all leads to the ruling of a fair ball and thus home run.