Umm ... isn't this solely about the action of the plane's engines and the fact that they push air through at great speed (science pushes, but it never, ever sucks

), creating air flow over and under the wings, and then the whole Bernoulli effect thing happens, and you get lift? So the treadmill plane should lift off ...
Am I remembering Physics 100 correctly?
otoh, will just the movement of air through the engines provide enough airflow to create sufficient lift for the plane to take off? Normally there's the engine push-through of air
plus air passing over/under the wings because the plane is moving relative to the atmosphere - on the treadmill it's not. Will there be enough air moving over the wings to create the needed lift?
Now if we could just get planes to land on little bitty treadmills, we wouldn't have to build long runways anymore!