Last tested: March 2021
No. Despite this being a very bad idea (why let everyone with a gmail address log into your Looker?), it also turns out it's not possible. This is part of why you want to own the domain(s) that you enter in the Google Auth panel.
The reason: When authenticating a user via Google Auth, Looker checks the 'domain' value for the user using the 'google_plus_api' api call to Google. But, it turns out that that is not set for gmail accounts. Those users are, apparently, not in the gmail domain in that way that other domain users are.