No problem if you pull your complete mailboxes using a tool like isync/mbsync. I have background jobs, in addition to regular backups, which pull to all my powered on computers every 30m. As long as the source is IMAP, it's very easy to not get screwed. I couldn't care less if my email hoster today would lock me out. I'll point my domain elsewhere and I have all the data as maildirs.