I don’t get it. I am not familiar with google drives.
Obsidian files are just regular files in the filesystem. If GDrive works like dropbox, there should be no problem.
Does google drive instead creates an encrypted folder on your harddrive and to access it you need to online and logged on?
Now that I think about, GDrive had the option of keeping VIRTUAL files on your hard disk and they are resolved to files in the cloud (downloaded on the fly) IF GDrive is running.
We don’t support this workflow (and most likely won’t implement first party plugin to support it)
If this is problem, you need to look into GDrive settings and configure so it actually maintains the Obsidian vault on your drive (not just virtual files).