I figured out how to get Outlook 2016 for Mac to fully sync with my Google G Suite account. At my work we use Office 365 but the version of Office 2016 for Mac is deployed from a volume licensing program. I tried downloading/installing Office 2016 from my Office 365 account but that did not work either.
I found the key is to make sure the About Outlook window says 'License: Office 365 Subscription. Mine didn't say that, so I downloaded the Microsoft_Office_2016_License_Removal_1.0 package from here:
https://support.office.com/en-us/article/how-to-remove-office-license-files-on-a-mac-b032c0f6-a431-4dad-83a9-6b727c03b193
I installed it to remove my Office 2016 license. Then when I launched Outlook, I got a window asking to sign in to activate Office, so I signed in with my work Office 365 credentials. I then joined the Office Insider Slow program and patched Office 2016. When I added my Google G Suite account, I got the Google in Outlook window mentioned in Sunder Raman's post on Monday, 5/21/2018. That allowed me to fully sync my G Suite account (email, calendars, contacts).
Thanks! If anyone is interested I created a How To document, message me your email and I send it to you.