by Ken Task.
Automated backups to Google Drive would be dependent upon platform upon which Moodle resides. If on Windows, for example, install Google Sync on machine that is setup to sync a Google accounts drive (assuming that would be yours). Once that is done, find the directory Google Sync is using. Then, in Moodle, set up a file system repo and point repo to the directory for Goolge Sync. Last step, automated backups setup that point to alternative location ... would be directly to the location of the storage for Google Sync on local drive.
So on a Mac or a Windows server ... easily done. On a Linux box ... it would take some work ... but any Linux OS that had Google Sync could be used the same way. Might have to have a GUI desktop to do it, but there might be a way via command line ... depending.
If on a shared server .. kinda doubt there would be a way, but ... ask provider about it.
'spirit of sharing', Ken