If users are moved from an org that has access to the Mail service, to an org that does not have access to the Mail service, then YES, their email is deleted after 30 days.
The easiest way to do what the original poster wanted, and you too Ed, is to upload a CSV file with new passwords for the users you want to prevent mail access to. You can do this right in the Dashboard, no need for GAM or anything else. You can use Excel to create the file, and also do a lot of the work for you (using functions to build the usernames and email addresses).
I have done this many times in the past and set all desired user passwords to the same thing, something like changepass385$#, that they will never figure out.
This method solves the problem in just a few mins, with no loss of data. The only drawback is that messages sent to these accounts will be "black-holed" to other senders ... no message that the account is closed, no bouncing.
Joel