[Phil^]

Actually, my analogy has given me food for thought.
In the running on treadmill example, the force is applied against the ground ( running ) , with a plane that force is applied to the air.

Im back to the "hmm, not sure" stage. It would need to be shown through experiment for me

perhaps the root of the confusion is in the wheels, so lets remove those from the equation.
Assume the plane's wheels and the threadmill surface are replaced with magnets of equal charge ( therefore the plane hovers ).
Would it take off now? I suspect it would