There is no native integration for Google Drive, nor is there an app to do so.
But... that shouldn't prevent you from setting it up if you have some Linux-skills. Basically you want to treat your Google Drive as a normal (network) external storage, and sync to it periodically. For normal external drives that is easily set up with RSync. For cloud storage there is a specifically designed tool called RClone.
Maybe the mods can verify, but I think you should be able to install it parallel to Volumio and set it up to sync periodically (like every night). Be careful with apt update and upgrade though.