Authenticating off Google accounts would have to be via OpenID as Olav suggested, that is Google's allowed method when you want to use Google as the identity provider, as discussed
here - though not the current OpenID moodle plug-in as it is not maintained, however it's code might help as a building block.
With OpenID, Google acts as the identity provider, which it sounds like is what you are looking for.
The tool Marc sent you to uses Moodle as the identity provider, with GoogleApps as the service provider as described
here - as an aside, the reason we designed the Google-MoodleSSO to use Moodle as the identity provider was that Google's OpenID idp solution wasn't ready when we were developing the integration - it is also nice in cases where you have an established method to get your users into Moodle and don't want to have to redo that for Google.
For a full solution SSO using Google as the identity provider and enabling users to see their Gmail inbox in Moodle, you would need a blend of both the current MoodleSSO tool - for the
Oauth parts that pull in data from Google, + an OpenID based SSO. If you write this, please post it back here, it would be great to have
.
