I have been bashing my head with this for a few days (Updated to 11.3, then get this Google Desktop error). It could be our corporate tools (we use Carbon Black), as it doesn't seem to be a consistent issue when I ask my peers. HOWEVER - I did manage to get it working, and it's a strange one this.....
I found that instead of clicking the dialogue to "Open Security & Privacy Settings" (as per screen shot). If you have that open already, and unlocked (as admin) and visible on your desktop. Now do the thing in Google Drive to connect your account (it opens in a browser). Close the browser window straight away, then the "Google Drive needs your approval to open your files" dialogue appears. DON'T CLICK the "Open Security and Privacy Settings" - instead, on the already open Security and Privacy settings dialogue for about 4 seconds, and for about 4 seconds only! - the button to Accept "Google Inc" appears. If you're quick enough, you can click it, a driver installs, the mac reboots and voilà!
Let me know if this works for you. Good luck.
Steve.