The conveyor does nothing. It's a fictitious monkey wrench. The conveyor would have to move faster to match the rotation of the wheels, but would also be adding to the rotation speed as it moved. So the effective ground "speed" (the amount of conveyor passing under wrt to the plane) would be insane. But, since the air over the wings and the plane thrust are completely independent of the ground and wheels, it will still have forward velocity and will therefore take off. The conveyor is not moving the plane backwards (and negating its propulsion/movement).

As mentioned, forget about the conveyor and the wheels - they're just there to get people down the wrong path. As can be seen by most of the posts in the thread and no doubt the dozens in the other forums where this has been posted. Reading too much into the question.

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The whole problem boils down to, does this conveyor belt keep the plane stationary with respect to the air?

The simple answer to this is NO. So we shouldn't even bother to think about seized wheels, hub friction or anything else. This is not the same as having no wheels on the plane where it rests on the conveyor. Nor having a pontoon plane on a fast current that's moving the plane backwards (so it would have to produce enough thrust to compensate for its reverse movement before it even generates positive/forward movement wrt to standing air.

I think I'll send this question out to a few dozen people at work on my last day...