We have wind gradient due to friction with the surface in the real world, and wall effect in wind tunnels which is much the same. It is therefore reasonable to assume that a moving conveyor belt would induce some movement in the air above it. Clearly the belt would need to be going a lot faster than normal take off speed to induce an airflow at wing level that is at take off speed, and the comments about tyre speed would apply. The aircraft would need to be restrained at some fixed point ahead of the conveyor belt to prevent it being shot backwards until it is in the air or engine thrust carefully balanced to match the drag from the induced airflow acting on the airframe.
As all the others have said, it is airflow over the wing that generates the lift that allows a conventional aircraft to fly, not speed on the runway. Here is a hang glider proving the point: