They do have it watermarked. If you open up a source Maya or file that was created in (or ever opened and saved in) a Student version, an alert will pop up. However this same alert doesn’t seem to occur with exported files such as FBX. However I’ve heard from a few forums and such that if you poke around in the plaintext of those files you can still find some hint at the license information that was used, but I have no first-hand verification of that myself.
I agree however that the ideal choice should be to go OS or with a budget option. But I have to say I don’t agree with this idea (Autodesk) of seemingly demanding that any work that was made has to be remade rather than just being retro-actively ok to work with once a license is purchased, which seems to be Autodesks’ opinion.