A plane's speed is generated by air thrusting devices (props or turbines). The wheels are freely rotating. A conveyor running opposite the plane will only double its ground speed, but will not significantly alter the air speed (I say not significantly because there will be some "drag" caused by the minimal friction of the rolling wheels. For the most part it's irrelevant though). The air speed is what is required for take-off.

Similarly, a plane in high headwind can take off at very low ground speeds. I've taken my model planes down to the airfield on very windy days and taken off almost without moving (relative to the ground).

Edit: Bleh, NOW I see BD-VX99's post.