The current version of Google Browser Sync (GBS) has an annoying bug that can bite you if you start Firefox before you have an active Internet connection, if you lock Firefox with a Master Password. Firefox starts, and prompts you to enter that password, but GBS pops up a 'dialog' that shows it's trying to connect ... and it can't, and the Stop button does not work.
So all you can do is force-quit Firefox, get on the Internet, and only then start Firefox.
Here's an alternative that I hope is comparably secure: get rid of that Master Password in Firefox, and, instead, create an encrypted disk image with Disk Utility. Give it a nice, long, strong password. Move Firefox to that disk image. Eject the disk.
Whenever you start Firefox (you can even put it in the Dock), you'll be prompted for that encrypted disk image password. After you enter it, Firefox will start. Now, even if you're offline, you can use Firefox. GBS will try to connect for a short time, then relinquish control and merely offer a button to 'Reconnect' when/if you decide to go online. You can click the X to close that GBS pop-up, and you're done -- Firefox is ready.
Mac OS X Hints
http://hints.macworld.com/article.php?story=20060627235124699