Good call Micromoog. That's largely on Kahler or Floyd Rose locking tremolos. If it floats (e.g. doesn't rest against the body when you aren't using it, as most strats, teles, and Gretsch guitars do) then it could be trouble. It won't damage the guitar, but it'll just make the fine-tuners incredibly finicky, and they're already bad enough haha.
Having owned an Ibanez RG570 for a few years (had a Floyd Rose locking trem), I've had plenty of personal experience with this. Great sounding guitar, for sure, but keeping it in tune took serious and tedious grunt work. Not to mention changing strings.
Oy vey, haha.