Will it fly?

[Evan]

Yes - its a theoretical question. The 'treadmill' is infinitely long. And for theoretical discussion purposes, the wheels/treadmill are frictionless.

well thats a completely different question.

the way it is phrased and illustrated above implies that the plane itself doesnt move.

the way you just changed it just means the runway is a big treadmill, which still means its a runway and will still take off with enough thrust, and isnt a particularly interesting problem.