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Conveyor Belt Runway

I've come across some previous discussions on an interesting question, interesting enough to repost with my own theories and assumptions.

Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway, and intends to take off. The conveyor belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

Can the plane takeoff?

The argument FOR the plane taking off is that planes are different from cars. A car uses the wheels for its forward motion. Thus, if the treadmill spins as fast as the wheels, the car will go nowhere. However, for a plane the wheels are simply there to reduce friction between the ground and aircraft. The force propelling the aircraft forward comes from the jet engine or propeller. The engine's force will propel the plane forward and the aircraft will takeoff with the wheels spinning really fast. As a simple example, think of a skateboard with a fire extinguisher on a treadmill.

The counter argument is that, while the plane propels not with the wheels but with the engine, the wheels still have a friction. Combined with the speed of the conveyor belt, the friction will counter the force of the engine. To simplify it a little bit, replace the wheels with skids. Certainly, there would be enough friction there to allow a treadmill to counter the aircrafts propulsion causing the aircraft to stay stationary. Going back to the wheeled aircraft, we have to make a couple assumptions. First, the conveyor belt will withstand the speed it must go to counter the aircraft. Second, the same durability requirement goes for the wheels. Third, the arm connecting the aircraft to the wheel must be sufficiently strong. The forces are being applied to the aircraft at different points. The propulsion comes from the back or front. The friction comes from the wheel. Fourth, the conveyor belt speed is governed instantaneously. This fourth assumption is the most important. If there is a delay between the wheel gaining speed and the conveyor belt gaining speed, there is a possibility for the aircraft to gain velocity and maybe takeoff. Given these assumptions (and likely a few more) the aircraft's propulsion should be able to be countered by the conveyor belt and friction.

I currently lean toward the aircraft not taking off given that we are talking about a hypothetical situation. Since the control for the conveyor belt is impossible to make, I'd consider the aircraft would take off in the real world. Your thoughts?