A treadmill moving in the opposite direction of the plane, but at the same speed as the plane will cancel out all movement of the airplane, making it stand completely still.
No it won't. A plane doesn't use drive wheels to accelerate like a car does. It pushes against the air with a propeller or jet thrust making wheel speed almost irrelevant, within the limits of the bearings and wheels ability to withstand the centripetal force that comes from rotation.