Assume that instead of a conveyor belt, that we have 1000000 idiots pushing the plane because they have nothing better to do. Also assume that the surface area of the aircraft is so high that and it's weight so low that take off speed becomes largely irrelevant. Since there is motion and thus airflow, the plane will take off. As long as the brakes on the wheels are on and the coupling of energy complete, it should fly.

The problem with the conveyor belt ideal is actually a transfer of power at the wheels, because it's well known that you can throw aircraft off other devices that deliver power, like the steam catapult on US Navy carriers. When you turn the conveyor belt, the wheels would turn in the opposite direction, but this assume the wheels are perfect and have no loss, meaning they turn the forward energy of the conveyor belt perfectly into rearward energy in the wheel, thus you have an equalibrium.

The great big question is, due to losses, it would move, but in what coupled direction?