A plane doesn't increase velocity by pushing off the ground; it does so by pushing off the air. The ground is just there to keep the plane from falling into the center of the earth. (Think of seaplanes ... they can still take off despite lack of significant friction with the ground). Since the air in this example is no different from a usual takeoff, the plane would push off it and move forward as usual. The difference, however, is that as the plane started to move, the wheels of the plane would turn, and the fictional treadmill would increase in speed to match ... which would cause the wheels to turn faster, thus causing the treadmill to move faster, etc ... a mutually reinforcing system, until the wheels and the treadmill both turned to molten lava (and how fast that happens depends on how closely the treadmill could match wheel speed). Meanwhile, the body of the plane would be busy taking off as usual, unaware of the drama happening below (except, perhaps, for the smell of melting rubber).
So there you have it - the definitive word on the subject. Except for my lack of any advanced degrees in the physical sciences. Anybody want to weight in?