Of course it will. The fact that the surface the plane is situated on is moving doesn't matter at all. The plane generates all of it's forward motion from the engines, not from the wheels. The wheels can spin all they want but the force that's pulling that plane forward is completely independent from the opposing force of the treadmill. If you had a plane on a giant ass treadmill, it would still move forward and eventually take off.
Of course, I have absolutely NO idea what I'm talking about, but it makes sense to me.
EDIT: Just thought of this. I guess it'd be like having a toy car on a treadmill, if you leave it there its gonna go nowhere or go shootin backwards off of it, but if you apply a force separate from the unpowered wheels, ie your hand (engines), with enough energy expended from you, you can still push it forward on the treadmill.