Is there a way I am able to put my guitar into drop D with a Floyd Rose?

Do you mean use the FR to execute the retuning on just the 6th string or do you mean will the FR work with the sixth string dropped to D? Try moving to a seven (or eight!) string guitar with the seventh string tuned to drop D. Then you keep all the top six string fingerings and have the low D whenever you need it. I can’t remember the guitarists name, circa Byrds, who developed a system of tuners that changed the pitch of a couple of strings, kind of like pedal steel.

Unlock the nut; probably isn’t going to stay in tune. Probably doesn’t now though. I’m a fixed bridge kinda guy.