The spirit of the original question centered on the wheels and conveyor moving at the same speed in opposite directions.
If you chock the wheels of an airplane with wheel chocks, will the plane move if it cannot roll the wheels over the chocks? No.
If the conveyor is spinning at exactly the wheel speed for any given RPM, the situation will become the same as if the plane had the wheels chocked. The conveyor spinning in the opposite direction will create a force that will nullify the plane's forward movement.
The plane doesn't need the wheels to fly, no. But it does need them to move along the ground while taking off. If they don't move, for whatever reason, then the plane doesn't fly.