I am still testing the lite version, so I need my GV number forwarded to both for now (so I can, you know, answer calls while I am out), but that sure sounds like the solution.
If you want you could use GrooVe Forwarder to automatically adjust your forwarding settings. When GrooVe IP or GrooVe IP Lite is signed in it can forward calls to Google Chat. When they are signed out it can be configured to forward calls to your cell number.