It's quite simply yes.
i drew a little picture to help you out.
A car moves because the engine rotates the axle of the wheels which is attached to the car. As the wheel spins, the car attached inches forward. That means that anything that subjects the wheels to a force will directly affect the car. If the road starts moving towards the back of the car (as on treadmill), then the wheels will continue spinning and the car will remain stationary because movement of the car DEPENDS ON THE WHEEL'S ATTACHMENT TO THE ROAD.
The car's speed is related to how fast the wheels can turn and inch forward. This means the wheels are actively spun by the engine. So if the wheels are the reason for movement and the road moves backwards and the wheels depend on the road, then the car will not be moving.
Wheels turn twice, the car is moved forward a few feet, but since the road goes back two feet, the car will remain stationary.
The airplane does not move thanks to the wheels. The airplane's movement is dependent on the turbines which propel it. That means that it does not matter how fast the wheels spin or how fast the treadmill spins. Since the wheels are not actively spun by the plane's engine, it is irrelevant what happens to the wheels.
The forces of motion are on two different planes (mathematics term) and not connected in anyway.
Since the wheel can spin somewhat freely and is not fixed to the airplane (not the same way as a car is), the plane will be able to move however it sees fit.
In the real world, the wheels would be spinning ridiculously fast and would probably melt or break off but we ignore that.