I'm gonna toss my two pence into this cause im in a debate mood
The question asked is if the conveyor is moving in the opposite direction at the same speed the plane should be travelling forward. (i.e. if the tyres are spinning at a rate to move the plane at 100MPH, the conveyor would be moving at 100MPH the other way) Oviously, to achieve this effect in the real world the conveyor would have to be motorised or designed like a rolling road like you see in a car garage etc... both would have exactly the same effect.
While the plane is on the ground, all the engine thrust is used to overcome the friction between the planes tires and the ground. Sufficient force will propel the plane forward. The forward motion on the plane forces air over the wings to generate lift. When the plane is travelling at sufficient speed the lift is strong enough to allow the plane to become airborn.
However, if the conveyor is moving in the opposite direction at the same as the aircrafts tyres. All that thrust the engines provide is transferred through the freewheeling tyres into the conveyor belt instead of the moving the plane forward. Because of this no lift is generated on the wings, therefore, the plane is completely incapable of taking off. The only way the plane could take off in these circumstances would be if the wind was blowing fast enough over the wings to generate the sufficient lift. But if a plane requires a speed of (for example) 200MPH in zero wind conditions, the head wind would have to be going 200MPH to cause the plane to lift off from a stationary position.
Think of it like a Formula 1 car sat on a rolling road. You can rev the engine all you like, all that will happen is you make the rollers spin faster all those aerodynamics will be useless because no air will be flowing over them. But a rolling road is rollers that are freewheeling. The conveyer for the plane would have to be motorised and controlled to allow it to travel in the opposite direction at the same speed the tyres are going.
Hell, replace the conveyor with a rolling road like in car garages and you've got exactly the same effect. All that thrust is transferred into the conveyor/rolling road through the tyres. The tyres are spinning which is the aim of the thrust but the ground is moving where as normally it isn't.
So simply put. If the ground (conveyor) is moving in the opposite direction at the same speed to keep the plane stationary, then NO, it will never take off.
Enjoy