Will the plane take off?
All the treadmill does is increase the RPM of the tires at rotation.  Airliner tires are generally spinning at somewhere around 800-1000 rpm at, say, 140 kt depending on the diameter.  If the treadmill is running at 140 kt in the opposite direction, the tire would have to be spinning at double whatever it is normally when the airplane achieves liftoff speed.

The question becomes:  


Can the airplane's thrust overcome the tire's increased rolling, bearing and brake drag (from casual brushing contact of the brake pads) friction when spinning at double its normal RPM?
Can the tire survive running at double RPM, well above its speed rating, without blowing up?


For:


Probably yes, but it would extend the takeoff distance quite a bit, but...
I would say probably not.  An airliner tire will have a speed rating that has a good margin above the normal operating speed, in the low 200 kt range, with probably some fudge factor above that. So it could probably survive up to, say 230 kt.  Taking it to double its normal operating speed, an RPM equivalent to 280-300 kt, is probably too much and there is a pretty good chance at least one of them would blow up.  Almost certainly if they were recaps, which most airliner tires are.