No, it avoids doing that (see the link someone shared above). Git actually also rarely overwrites files. The only case I'm aware of are refs, so I think it could happen that a if you modify a branch on two machines and then sync via Dropbox/rsync, one of those changes could get lost.
Ah, you mean to share the repo you are issuing git commands to directly. Yeah I would expect this to cause problems. Surprising to hear that JJ supports this.
This wasn't what I was talking about, I meant that you should create a bare repo and push to it, not that you work directly in a directory in Dropbox.