The problem with your flawed analogy is that a car is propelled by it's wheels, where as a plane or jet is not. The speed of a treadmill is a moot point. The wheels (which are the only contact points on a plane or jet to the ground) are free spinning bearings. Keep in mind that a plane or jet derives it's speed relative to the ground, not the spot where it touches the ground.
I see that you are right in a sense but i still doubt that the plane would take off.