The confusion arises when you factor in the wheel speed. As stated, the problem doesn't talk about wheel speed. But if it did ...
Regardless of where thrust comes from, if the wheel speed is what was matched by the treadmill, then no, the plane would never move. It isn't possible for something to move forward if the two speeds are the same. That would be the same as a pilot maintaining just enough thrust to keep the plane stationnary.
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