Someone will, of course, claim Google would never do this, but this presumably would make it trivial for Google itself to log into all of your accounts. In many cases they are already syncing a copy of your passwords.
The sort of thing as a tech crowd would horrify many of us, but the public would largely go "oh neato".
No, that gets them the full way there. They have your 2FA codes, and if you use Chrome and opt into it syncing passwords for you (passwords.google.com), this gives them both pieces of the puzzle.