[Lewisham]

FWIW I believe Takeout does work when your account has been disabled, so that you can transfer to another provider.

EDIT: Although sadly it looks like Gmail is not part of Takeout :/

[bmj]

Right, Gmail is not part of Takeout, but there are third party apps to facilitate this:

http://gmvault.org/

http://www.gmail-backup.com/

[trhtrsh]

Ever mail client written since ~1990 is capable of downloading your Gmail.

[Lewisham]

The problem is that if your account is disabled, it's unlikely you'll be able to acces Gmail, IMAP or otherwise. I think Takeout has an exception so that it works even when your account does not.