Sometimes if you wait a little bit, the Google Drive synchronization process will complete, and you can then exit and backup. Google Drive tries to synch the file every time it senses a change, so when you change something in the database, Google immediately synch's. Waiting lets that process complete and then you can exit with backup. At that point, your backup should have first priority, and Google will immediately synch after it completes.
If you hover your mouse over the Google Drive icon in the system tray, it will tell you when it has completed.