Content Manager currently has no integration with Google Docs. This sample explores what is possible within the constraints of the Google Docs add-on ecosystem. It turns our quite a lot is possible, much more than with Gmail.
The sample below demonstrates registering and updating a document from Google Docs to Content Manager. The code for this sample is available on the community repo.
If you have any thoughts on the importance of Google Docs support or the details of what a Google Docs integration should do please contact me.