I doubt that any database synchronization software could reliably synchronize (at the database level) changes you make in 2 copies of a UR database, and that's not something we have the resources to implement. I think your best option would be to ensure that you're always working on the latest version of the URD file by waiting for Dropbox to sync it before editing. Also make sure you're setup to minimize updates to a database while open in UR:
http://www.kinook.com/Forum/showthread.php?t=3728