It seems like everyone's stating variations of the same two things. I think the problem is that the original question's description isn't specific enough.
Originally Posted by b00gers
This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction).
Group 1: People who assume the plane does NOT change position
Forget the idea that the airplane will move forward anyway, the idea is that this is an imaginary conveyor that can somehow magically keep the plane in the same place. The airplane doesn't change position AT ALL. Not changing position at all means no air flow which means no lift. I think this is what the original question assumed.
Group 2: People who assume that the plane DOES change position
The idea here is that realistically, a conveyor belt won't keep a plane in the same position because it doesn't rely on it's tires for thrust. It is assumed that the airplane will eventually overcome the opposite speed of the conveyor belt, reach a takeoff speed, and take off.
Personally, I belong to group 1 because I think that the original question makes certain assumptions. I think it is written simply enough to assume that the airplane was to be stationary with respect to the air around it. But I guess it all comes down to how literal you want to be about it.