You guys seem to all be assuming zero friction between tire and wheel. There is friction. If you were able to somehow feather the throttle up slowly while increasing the treadmill speed, the friction of the wheels of the plane on the treadmill will exert a rearward force which could easily be countered by an increase in throttle. I've flown a plane and it doesn't take much throttle, once rolling, to keep plane moving down the runway at a decent speed and that is with wind resistance. Without wind resistance, throttle percent won't be nearly as high because the only friction to overcome is the treadmill.
All that said, planes work on one simple principle: lift generated by wind moving over the wing's airfoil shape. Without that lift, they plane is going nowhere. It doesn't matter if the treadmill reaches 300 miles per hour and the plane is running throttle at 30% to counter the friction. There is no lift without AIRSPEED.
This seems like a particularly silly myth to try to prove/disprove...








