Again, make sure you are picturing a conveyor belt that is as long as the runway. The plane will simply take off as normal, in the usual distance, but the wheels will be spinning twice as fast due to the opposing speed of the conveyor belt. The belt is ONLY affecting the wheel speed, not the planes airspeed relative to the earth.
Imagine you have a model rocket. Instead of pointing the stand for it straight in the air, you point it parallel to the ground. Hit the switch, rocket engine fires, and the model takes off. Due to lack of steering, gravity may pull it straight into the ground, but it will still become airborne, even if the stand is mounted on wheels and on a conveyor belt.....