Sure, I'm not suggesting there would be permanent data loss... but doesn't Dropbox renaming a bunch of files deep within .git folder result in an unusable repository that you'd have to fix by hand or restore from backup?
This whole discussion made me curious, so I tested it. Dropbox doesn't rename files. It creates new files. All you have to do is delete the new files (which are really "forks" of your current data) and you have your working tree synced with your data store again. It's really easy.