I can't say for 100% sure,

But i dont think it would do any good, the constant change in tension on the neck could distort the wood, which is costly to repair.

going from standard to drop D alot should be fine, as its only one string down half a step, but anything lower I would recommend that if you go down, stay down.
yeah i know that drop d is fine. but my high e string is the one that is a problem, it refuses to go up easily if i'm tuned to D standard or something. when i get a new string i'll go easy on the drop tunings i think.
Yeah probably a good idea, maybe even think about saving for a new guitar and having one of them dropped, just put thicker strings on it.

If you really really need to drop tune your guitar now, when you come to replace the strings, go for a thicker gauge.

Does it have a floating tremolo? because they are NASTY to change string gauges with, and constantly detuning will mess it up.
i don't have a floyd but it has a trem. i will keep this guitar and put a set of heavier strings on it and keep it in D standard and lower after i finally get a new guitar.