OK...how about this.

Regardless of whether a wheel is driven through a drivetrain or rotates freely, it covers a given distance per rotation. In this scenario, the distance covered per rotation is reduced to zero because the treadmill moves that distance back as the wheel tries to advance forward. Again, this is true regardless of what's driving the wheel forward.

So the relative forward motion is zero, the relative wind over the wing is zero, airspeed is zero, and your chances of taking off are...you guessed it...zero.