I have this and have been unable to login since 2015 with no ability to recover my account (I know the password, but it's flagged as "unrecognized device"). I also can't turn it off or delete the account.
Good question. I'd be fine if that account stopped storing mail as long as the forwarding kept working.
I do the same thing but I think it's all the same for Google, if you don't actively log into Gmail they can't know for sure that it's still being used. We'll just have to remember to log into the service once every other year.
I hope they'll bother to send a warning email at least.