Hi 39 & MrW
I believe that if you started the belt with the plane's engines off, the plane would remain stationary. The wheels would move, but not the plane, thus leaving the plane free to propel itself along the belt and take off.
To explain: my point is that the planes engines act on the air, not the wheels.
If we then agree that the moving belt acts on the wheels, not the plane and the plane would remain stationary if the belt was moving, then it would be free to move forwards and take off simply by applying thrust.
Correct in every way, but you forgot to mention as a consequence of the plane moving forward then the wheels would turn forward more than they are doing already, at which point they aren't in sync if you like with the belt speed