[BTurk]

I'm seeing two different interpretations of the question, which is the difference between landspeed (speed relative to treadmill) and airspeed (speed relative to a fixed point on the surroundings, say a building)....

A.) If you think of a plane on a treadmill the length of a runway and light the engines and turn on the treadmill. Then yes the plane will take off, the landing gear are only hooked to brakes, no kind of driving motor, the plane will overcome the conveyor and thrust forward (the landing gear will be turning at twice the speed of the plane, which may cause some other issues..durability, perhaps??) but eventually the engines on the plane will overcome the treadmill and theplane will take off (twice the amount of thrust as regularly needed). In this case land speed (speed relative to treadmill) will be twice that of airspeed but the correct airspeed would eventually be achieved and the plane will take off.

B.)If you are assuming the intent of this theoretical conveyor is to keep the plane stationary to a fixed point outside the conveyor (landspeed = takeoff speed, airspeed = 0), then the plane would be generating the amount of thrust needed for take off but have zero airspeed, meaning no pressure differential over the wings and no lift force, thus no take-off.

It will be interesting to see how they model it...