I have read every post and switched sides a dozen times. I have come to the conclusion that the plane will take off. Here is how:

Imagine there was no ground. For all intents and purposes this is what the original scenario would be like. If there was no ground and the plane was somehow suspended in mid air would it be able to take off? Yes. The engines or prop would still propel the plane through the air.

Back to the original scenario, to an observer it would look like the plane was sliding along the conveyor propelled by the engines until take off. Wheels and conveyor moving in opposite directions at the same speed.

I lost it until I realized that the wheels are meaningless for moving the plane. All they do is keep it upright and off the ground until the plane can take off. Keep telling yourself that the wheels do not move the plane or have anything to do with its forward propulsion.