Correct me if I am wrong, but a plane gets lift from the fact that the air passing over the top of the wing, has further to travel than the air beneath the wing. This means that the air above the wing, is of a lower pressure, than that below. This imbalance, creates the upward force on the wings, enabling it to fly.
If the plane, has zero speed relative to the air it is in then this imbalance would not occur, and there would be no upward force.
The OP stated that the 'conveyor' would compensate for the increase in speed of the plane, by increasing its own 'counter' speed.