The way I see it, the problem can be broken into three parts, none of which are equationally connected to each other. That of the plane's fuselage and it's relationship to the air, that of the wheels and their relationship to the conveyor and that of the fuselage and its relationship to the wheels. To simplify the problem, lets consider the wheel bearings to be frictionless (no heat/can't lock up/cannot induce movement on their own accord).

Part I: The wheels/fuselage relationship.
The wheels sit under the plane and provide a "frictionless" support between the fuselage and the ground. Since the ground is "stationary" and the plane must move to attain lift, the wheels break all physical connection between the fuselage and the ground while it is overcome by gravity (lift comes later).

Part II: Wheels/Conveyor relationship
Consider that the wheels have perfect physical connection to the conveyor through friction (no slip). According to Newton an object at rest remains at rest unless acted upon by an outside force. So, when the conveyor moves, the wheels turn, but, because of the fricionless bearings, have no effect on the fuselage. This induces relative motion between the conveyor and fuselage, but no true motion (speed over geographical ground) or relative motion through the air (still no lift).

Part III: Fuselage/Air relationship
The fuselage is connected to the engine. The engine has an output shaft that is connected to a propeller. The shaft is coupled to the engine by another frictionless thrust bearing. This means there is a physical connection between the propeller and the fuselage. When the propeller turns, it cuts the air causing a low pressure area to form on the front of the propeller and a high pressure area on the rear. Because of this pressure differential, the propeller pulls forward taking the fuselage with it.

The outcome:
Because the propeller is now pulling the previously stationary object forward, it is achieving relative motion with the motionless air (no wind) and static geography. As the plane moves forward and relative motion between the fuselage (with wings) and air increases speed, vertical lift occurs and takeoff is achieved. The key is that the wheels do nothing in this case except keep the fuselage from making physical contact with the conveyor while lift has not overcome gravity.

I hope I made my thoughts clear as mud...