An objects forward motion is defined by the object applying the force being exerted and the medium its being applied to.
So the answer here will come from following the force in both directions.
The force is coming from the propeller spinning.
The propeller is attached to the plane.
The force is being applied to the still air around the plane.
The air will move reward, and thus the plane forward.
The plane being on the treadmill has absolutly nothing to do with its forward motion and will only apply a small but insignificant amount of friction for the plane to overcome before actully moving forward. the only the plane WOULDNT move forward, would to be to spin the wheels fast enough to create as much force of friction, as the engines produce in thrust.
But the question here is what if we match speed for speed. So lets say the max speed of the plane is 200mph.
If you move the tread mill at 200mph, then apply full thrust to the engines, the plane will still move forward as long as the friction created by the wheels against the ground doesnt create a larger force than that of the engines thrust. This is almost impossible. So it is a safe bet to say the plane will move forward and eventully take off.