The only way to prove this, though, would to find a planet that has no day/night cycle, and see if those organisms have any sleep behavior.

Deep sea hydrothermal vents provide this experiment on Earth. While the ecosystems are not completely isolated from our sun based ones, they are pretty insolated from it. Of course, to actually prove this you would need multiple, independent, evolutions of life with a day/night cycle and multiple evolutions without one.