A swan could take off on a treadmill.
Although it wouldn't move forward under the power of it's feet, it would remain stationary untill eventually its wings would create enough lift through flapping to enable it to begin to move. It's feet are only in touch with the water briefly (or in this case, tredmill) and the wings do the majority of the work. Additionally, the swan doesn't take off by wind speed over it's wing, but by down force from flapping, so eventually it would lift.
Mind you, the speed of the tredmill would probably rip it's feet off when it touchs it as it approaches take off speed…