I have come to the conclusion that the aeroplane will take off in the aeroplane conveyor-belt problem.
The forces acting on the plane are thrust from the engines.
The conveyor-belt will simply make the wheels spin much faster than they usually do.
The purpose of the wheels on aeroplanes is to reduce the frictional effects that act in the opposite direction to the thrust from the engines.
These frictional forces will not be greater by virtue of the wheels resting on a surface moving backwards relative to the aeroplane.
*Is the British usage "conveyer" or "conveyor" ... ? I wouldn't mind except I'm very obviously using B.E. in "aeroplane" and I'd like things to be consistent.