I remembered @simon dug into this a while back. This is what he said:
A deactivated user will not receive email notifications for group messages or group mentions. A suspended user will not receive email notifications for group mentions, but they will receive emails for PMs that are sent to the group.
I’m not sure if this is intentional behavior, or an oversight in the suspension design. It sounds like deactivating and suspending a user will ensure that no emails are sent to them without having to remove them from the group. This may not be immediately clear to a mod/admin, though.