Same with Microsoft. I have a Microsoft account for a Gmail address, but Microsoft doesn’t realise that they should disable Outlook, leading to the funny weird situation where you can log in to Outlook.com with a Gmail address and enter a completely useless empty mailbox. I bet Google has the same quirk.
Alright, I guess I could enter IMAP or POP details and use Outlook as some kind of email client by proxy, but that’s an even worse idea.