What a cracking thread. 3 pages and people still disagree. Normally one side has won by now in this sort of riddle/question.
I say the plane will take off. Unlike a car, where power/force is provided to the wheels, the power of a plane is acting against the air. If a car is above the ground by 1mm, and it's wheels are spinning at 100mph, it won't move. A car is reliant on the ground to move. If the ground is moving against it at 100mph, it will be stationary.
However, if a plane is 1mm above the ground, and it's prop is providing 100mph of thrust, it will move at 100mph. It's forward thrust/power is independant of the speed of the ground. If the ground is moving at 100mph against it, it will provide a force against the direction of travel, but only equal to the friction imposed by it's counter-rotating wheels which are not attached to the drive train (like a car). This force is not affecting the planes method of thrust.