Applying real world physics to it the plane will not take off until the threadmill motor breaks down and the plane gain airspeed/relative to real ground speed.
Applying retard physics to it, where the wheel bearing somehow became totally frictionless and thus effectively removing any physical contact between the plane and threadmill, it will take off.
Misunderstanding the question and beliving that the threadmill is not powered by it's own motors and trough sensors match the airplanes relative to ground motion but instead is just free floating and would be powered by any thing such as the rotational motion that carwheels would apply to it to push it back makes the plane fly too as it's propelling force is drawed upon from the air, not the ground.
the correct answer is of course the first. the third makes you tragically misunderstood and the second makes you a plain old fashioned retard.