Well, yeah, its an airplane. If you meant will if fly if its engines are on, but the treadmill is moving fast enough to counter the thrust so its staying on there like a person running on one? no. Whether or not it flies has to do with how fast the air is moving across its wings. (although this seems nearly impossible unless the brakes were engaged) If it were a powerful fan that gave a strong enough headwind to keep the plane in the same place even though its engines were on, then yes it would fly, because the air would still be moving across the wings fast enough for flight.

Well according to the Mythbusters it will work.

if the plane did not move forward, like a car on a treadmill, it would not fly. as mythbusters showed, it will fly because the engines are pulling it forward, the wheels have nothing to do but spin, and offer little resistance .

The thing that makes planes fly is something called lift. Lift is achieved when air is moving across the wings. In this case the wheels of the craft are moving but it is still stationary and there is no air movement. No air movement= no lift= plane on ground (or treadmill)

Yes, it will fly, assuming it doesn't hit the handles and what not of the treadmill ;-) Anyone who tells you it will not fly does not understand fully how a plane works. The ground is COMPLETELY inconsequential. A plane moves forward because the engine (be it propeller or jet doesn't matter) pushes air behind it, this generates forward motion. Depending on the type of plane the engine may or may not help to directly force air over the wings (thing propeller...) but either way the forward motion forces air over the plane's wings and generates lift. On planes, the wheels are free spinning, NOT powered. Therefore it doesn't matter how fast the treadmill goes, the wheels just spin in place (once initial friction is overcome of course). A good example that may help... Think of standing on a treadmill while wearing skates. You are holding onto a rope the other end held by a friend who is standing off the treadmill. You can turn the treadmill on full speed and if your friend pulls on the rope you will still move forward. This of course assumes you can balance and what not. The rope is the engine of the plane, it pulls you forward but has NO connection to the ground.

well, actually, friction is more complicated than that. If you were to get the treadmill going at some crazy speed, you might overcome the power the engines could put out with the force of friction. It would depend on the power of the engines, and also would be rediculous to do, but it might be possible.