Yes and no... we have normal filesystem backups, but with something that changes as frequently as email, they might not be complete. We'd definitely have accessible backups for at least a couple of weeks (though if an email wasn't there long enough for them to show up in a filesystem "snapshot", it might be gone forever). Basically, if an email is in your mailbox for longer than an hour, we should be able to recover it if your local copy fails, and you can even recover it yourself (see the "snapshot" information in kbase).
Beyond that length of time (2-3 weeks), it would be much more difficult for us to get you a backup.
You might want to take the extra step of using "mailutil" (should currently be installed on all user machines) or a similar program to export mbox archives of all your mailboxes - you can then archive and compress them, and save them both on your local machine and on your server. That should leave you pretty well covered.