“The planes propeller and the conveyor create an equal and opposite force on the plane and its resulting movement will be nil.”

The thing is, the wheels underneath a plane freewheel. They’re just on bearings, and have marginal friction. Because of this, the conveyor doesn’t actually create any force on the plane. It’s similar to having glasses on a table, with a table cloth beneath them. If you jerk the table cloth out from under them, they remain in place.

As the conveyor increases in speed, this effect becomes greater and any force it does apply on the plane in reverse diminishes. Meanwhile, the force being applied by the propellor is increasing. If the friction between the plane and the belt is sufficient to equal the force produced by the engine, then it will remain stationary. But because the wheels rotate freely with minimal friction, the plane will take off with little difficulty.