It will take off. There need be no debate. For the reason why, which reads much more complex than it is, read the following:
Even if the plane starts off moving backward in relation to the ground, the propellor, when engaged, will begin to slow the plane in relation to the treadmill, and eventually overtake it entirely. Once the plane itself is moving at twice the initial speed of treadmill relative to the ground, that being it's own takeoff speed relative to the ground, it will lift normally.
That is the most extreme scenario. Even if you are calling the airspeed relative to the treadmill, simple physics allow the plane to take off. Unless you nail it to the treadmill or stick it in a vacuum, it's going to lift off.
So long as the wheel bearings are good for twice the liftoff speed, there will be no issue at all.
It's like mounting rollerskates to the side of the space shuttle. It's not going to affect anything in any appreciable way.
It doesn't just seem simple. It IS simple. Every forum I'm on has been discussing this. There is nothing to discuss. It will take off.
Cheers,
Kennith