However, if the plane has no flaps, no ailerons, no other moving control surface and can not modify its initial shape in any way or suddenly drop ballast, then will it take off?
If the angle of attack remains constant, then no, because as soon as it reaches a speed where the wing develops enough lift to support the weight, it will loose traction and slow down.
However, if the positions of the C of G, C of P, and mainwheels were adjusted correctly, you could arrange for the aircraft to pitch it's own nose up when it reached a certain speed, and fly a few metres before it ran out of 'momentum'.
MJ