I have a local branch for day-to-day dev work in git. My workflow is:
Rather than relying on Dropbox to synchronize all the files of a git repo, I would rather use git bundle, which produces only one file (including all your private branches), and sync that file with DropBox.
See "Git with Dropbox"
In "Backup a Local Git Repository", Yars mentioned having sync errors with Dropbox.