It would only stop the take-off speed if the plane got its thrust through the wheels (like a car).
This scenario would work with like, an F1 racecar for instance. If the treadmill was going ~200mph, and the car's top speed was ~200mph, it would not be able to move (not taking into account the wind factor which would actually allow the car to go above its normal top speed anyway).
Think about the plane. It interacts mostly with the air, and the air will still not be moving. Directly above a treadmill, the air isn't affected at all. Since the propellor (or whatever) will be spinning in the air, and forcing air backwards, it will push the plane forward since there is hardly any friction in the wheels (assuming they are properly lubricated)







