This experiment has different outcomes depending on how you set up the situation. With no friction, the airplane will always take off. But then you have to take into account that with out friction, lift won't be produced by the wings, etc... You can't just say, well, there's no friction here but there is friction here.
If the conveyor belt matches the forward speed of the aircraft's fuselage/wing, the airplane will take off with it's wheels spinning two times faster than a normal takeoff. This would maybe blow a tire, maybe not.
If the conveyor belt matches the rotational speed of the aircraft's wheels, as soon as the airplane starts to move forward, the wheels will instantly reach an infinite speed. At infinite speed, the wheels overheat and explode instantly and the airplane falls to the belt without wheels. Now because there are no wheels to control the belt speed, the belt stops and the airplane starts to skid down the belt and eventually takes off. Obviously, to do this you'd have to have a very overpowered airplane to overcome the drag of sliding without wheels.
So regardless of how you set up the question, in real life, the airplane will always take off. Well, that is if you have a big enough engine and the tire schrapnel flying at an infinite speed doesn't destroy your airplane.