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Is there anything preventing you to add gmail address?
No. I can add an ordinary gmail.com but when I go to add a G-Suite (Google Apps email domain I get the error message, 'your Gmail account is not configured properly. Please log in to your Gmail settings, go to the Labels section, and turn on "Show in IMAP" for your folders. But it looks like google has changed its settings in Labels
 
Idk much about google suite gmail domain address but I guess it does not work as the same way as normal email address?
 
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