Can I use Google Drive as Database?
Yes, it's possible to do that. It will work fine, because each user has their own data in their own drive. You can store as much data you want in that special folder, as long as it doesn't fill the entire drive quota.
Personally, I've done this using spreadsheets for my "database". I don't query directly the spreadsheet. Instead I incrementally sync it to a local DB on the device and only read starting from the last row I synced last. Very fast to sync like that.
You don't say where your app runs, but on Chrome desktop you even have a Chrome filesystem sync which stores in the user's Drive and syncs automatically to other chrome devices.