I think I'm going to weigh in and agree with omg, Origin and the rest who say the plane will take off. The essential point to remember when talking about a plane is we're talking only about the motion of air around the wings, not the motion of the plane relative to the ground. The propellars or jets from a plane only serve to cause air flow, they don't do anything to make the plane move. In fact, the only reason a plane moves forward at all is because its continually falling towards the ground and being lifted back up by the wings. Just as an aside, a rocket engine is different because it causes thrust directly with thermal energy, instead of moving the air around.
Look at it a different way. If you have a plane tied with a rope to a stationary object, and then you use big fans in front of the plane to cause air movement, the plane will eventually take off. This is how wind tunnels work. In this situation, the plane itself is stationary while the wind around it is moving fast enough to cause lift under the wings.
Now, think of the fact that both a propellar and a jet engine are designed to move air from the front of the plane towards the back. The only difference being that a propellar blows the air directly over the wings and the jet engine just blows it out behind the plane. In both cases, pressure differentials in the air will cause it to flow back behind the plane, just like a floor fan causes air flow in your house even though the fan itself doesn't move. Even if the plane could be held stationary relative to the ground, using a conveyor belt, the engines themselves will create airflow and once sufficient lift is generated, the plane will take off.
Here's a good link explaining relative velocity.
