Basically you can think of the wheels as just something used to create a low friction surface for the plane to sit on. In snow, skiis would work instead of wheels. With the treadmill going backwards and the thrust of the plane pushing it forward the wheels would just spin faster but the plane would still go. I imagine there would be a bit of resistance at first, since no wheel bearing is 100% perfect. So plane would probably start to go backwards a bit but then the thrust would overtake that motion and it would go forward.
That’s assuming a plane that has free spinning wheels. I’m not sure if there are planes where they actually do use motorized wheels to assist take off, if there are, then those planes would probably have trouble taking off. But no matter what for a plane to work it needs to be able to provide enough thrust to create enough lift to stay in the air, so even such plane would eventually take off, just use more run way.
At least that’s my guess.