I started (for the first time) to read the other thread. It's amazing how many demonstratably incorrect things people were saying.Not really true. It's air speed over the wings that creates lift. Jet engines produce thrust which propels the plane along the ground until such time as sufficient air speed creates enough lift to take off. If the treadmill negates any ground speed, then there will not be enough air speed to create enough lift.
Different story for small (ultralight) planes. The interesting question would be about small prop planes. I don't think the prop is large enough to create enough air movement over the wings to create enough lift without ground speed. It's not like helicopter sized props -- which literally move enough air by themselves to generate lift.
So let me apologize. The statements I made were specific to the case where the treadmill is capable of maintaining 0 ground speed. I believe that is the spirit of the question (it would have been clearer to say that the airplane is not allowed to move forward relative to the ground -- perhaps by blocking the wheels).