is workgroup safe to use on my computer, ie synchronizing to google.

Workgroup is safe to use providing that your computer is patched with all security updates from Microsoft and you have anti-virus protection software. Having computer behind a router adds additional level of security.

Really doesn't matter if the system is on a domain or a workgroup as long as the system is secured. Antivirus, windows updates, firewall, disable unused services etc is important for security