As a member of the yes it will take off club, I thought it was an interesting video.
But it did not, and could not perform the experiment as described in the original question.
What was very salient however, were the pilots words "we took off as normal". IE. their was no drag backwards, and no extra power was needed to take off.
Which proves that the wheel speed was irrelevant, Newtons third law of motion moves the plane forward, irrespective of what the wheels are doing.
So I believe you can now choose from 2 scenarios.
1) In a real life experiment, its just whether you think the wheels could survive the speeds generated.
2) In a purely theoretical argument, let the wheels do an infinite speed , the plane will still take off.
And johnD ,where I think your argument fails, about the impossibility of the question, is that you are considering a plane doing 1 mph and trying to hold station at 1 mph, and yes the wheel speed would build up very quickly.
Whereas in reality we are considering a rapidly accelerating plane where the conveyor will be playing catchup. The conveyor will have 15 to 20 seconds to impart as much speed as it can.