[Fasterthanyou]

The plane will take off because the conveyor is tracking the plane SPEED (not velocity) but since the wheels (friction or not) have no influence on the plane position then they are out of the "system of influences."
It says the plane moves in a direction. Well where does it say what moved it from a standing? Was it by it's OWN power? If it moved in a direction then it must be under it's own power and it must be moving no matter WHAT the ground is doing . Hence it will move along the runway and fly. In a real world you could say most planes wouldn't take off because the tires would blow-out or the friction in the bearings of the wheels would seize... but this is a theoretical question so those things are neglected and even if they weren't there are planes that take off at very low speeds.
In other words, the wheeld don't do **** so stop talking about them as if they are an influence.
You need to know the difference between speed and velocity for any of this to make sense.