[sperry]

Here's my answer:

1) The plane needs airspeed to generate lift and take off.
2) The plane's engines generate thrust by pushing against the air.
3) The plane's wheels (because the brakes are off) cannot enact a significant force upon the plane against the thrust vector of the engine.

Therefore, the plane will take off. The treadmill has nothing to do with the solution.

I dare you guys to prove me wrong without getting into rediculous agruments like "well if the conveyor is going 1 million mph the friction of the wheel bearings is so high it can't take off". The frictions/inertia of the wheels is insignificant with regards to the magnitude of the engine thrust.