I haven't read the whole thread, so this might already have been explained:
The plane should take off, as the wheels are free rolling. However, the treadmill must be long enough or the plane will simply fall off the end and crash.
Example:
Treadmill is moving at 100mph.
Plane's engine provides enough thrust to move the plane at 100mph (and let's say this is enough to take off with) in the opposite direction of the treadmill.
Plane's wheels spin at 200mph while the plane takes off at 100mph.
But as stated, this will only work if the treadmill is long enough (as long as a runway) to allow the plane ample distance to accelerate to 100mph in order for appropriate lift to build.
The treadmill and wheels don't create lift, the forward motion of the plane's wings through the air does.