Sync Google Drive when not logged in

Have you tried the Task Scheduler?

http://www.nekocreation.com/sync-google-drive-when-not-logged-in/

From above:

Google Drive will only sync your files automatically when you are logged in to your account on Windows. If you want Google Drive to start even before you are logged in to your account, you can add it to Task Scheduler.

1. On Windows 7, go to Start > All Programs > Accessories > System Tools > Task Scheduler
2. Click on Create Task…
3. Under General Tab
4. Name: Google Drive Sync
5. Security options: Run whether user is logged on or not
6. Under Triggers Tab
7. Click ‘New…’ button
8. Begin the task: At startup
9. Click ‘OK’ button
10. Under Actions Tab
11. Click ‘New…’ button
12. Click ‘Browse…’ button
13. Locate googledrivesync.exe (By default it is under C:\Program Files (x86)\Google\Drive)
14. Click ‘OK’ button
15. Under Settings Tab
16. Uncheck ‘Stop the task if it runs longer …’
17. Click ‘OK’ button to save the task

I believe you would have to run the sync client as a service. To do so, you can use Sc.exe.

I can't test this but the syntax should be something like this (from an elevated command prompt):
sc create GoogleDriveService displayName="Google Drive Service Wrapper" start=auto obj=WINDOWS_USERNAME password=PASSWORD binPath=PATH_TO_GOOGLE_DRIVE_EXECUTABLE

Piece by piece:
sc: creates the service
create: command to create service (see also, delete)
GoogleDriveService: a string you make up to give the service a name
displayName="Google Drive Service Wrapper": string shown under Name column of services.msc
start=auto: start on boot
obj=WINDOWS_USERNAME: Windows account that is syncing with Google Drive
password=PASSWORD
binPath=PATH_TO_GOOGLE_DRIVE_EXECUTABLE

@martin There's a bug in Googledrivesync that disables restarts if the "Start on login" switch is enabled in the preferences panel. That's why it's flashing when you restart it. (I would have put this message in the comment thread where it belongs but don't have the points to do so.)

To use Window's task scheduler to control GoogleDriveSync, disable the auto start option in the app's preference panel.

I specifically don't want GoogleDriveSync running most of the time as it interferes with other scripts that create and delete temporary files in the folders GDS backs up. Rather than rewrite the scripts to use a temporary folder outside of GDS's purview, I use the Task Scheduler to control when GDS does and doesn't run.