I don't see an option anywhere though, perhaps some hack.
If not, can this be a feature request?
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It's possible. Head over to your profile -> Click on Edit Profile & Settings -> Click on
My Logins ->
Add More Logins. Now select Google, and proceed to login to Google with the preferred Google profile. This will be added to Stack Exchange as one of the available logins.
As Rebecca mentions in a comment below: Be sure you log out of your Google Accounts first!