>>1062763No and yes.
As shown, complete with treadmill uprights physically blocking the wings and general forward progress? No, it would either roll off the back or build enough thrust to hit the uprights and then stop forward momentum (and thus the airflow over the wings and associated lift) unless the plane has enough thrust to drag the entire treadmill forward to suitable speed as well, which I doubt and assume is NOT a factor of this exercise, however amusing/terrifying it would be to witness.
Taken as an abstraction for "plane on a treadmill running opposite it's intended vector?" Sure, the plane could takeoff despite running against a treadmill; ----- just don't set the brakes.----- Treadmill rolls backward, engines thrust forward, wheels spin fast but basically free and the engine thrust overcomes the token wheel friction attempting to drag the plane backward and instead moves the plane forward relative to its initial position. Build forward velocity until airflow over wings generates enough lift to raise the plane and you have yourself a pretty standard takeoff, just with a little more wear on the wheels and such than on an unmoving runway.