I don't think the plane would take off if it were on rollers as you describe. The point of the experiment is that the propeller moves the plane down the conveyer until it reached take off speed relative to the ground. The conveyer has to be looooooong because the plane is moving forward as a result of the propeller.

The plane has to move relative to the ground to take off. The difficulty in this is that at first thought, one believes the propeller will not be able to accelerate the plane on the conveyer.