That's a question that you need to ask the email provider. Ask them there policy on email storage if a disaster happens. That's something that they can tell you better than us. As far as backing up the email locally using .pst files, to my understanding backups your local mail that you've already received. Most email accounts that are stored on the server are backed up either weekly or monthly and are saved as inbox.saved or something similar, that way they can backup your email if anything happens.
You can do a test, and see what happens. Create you an email on the email server, and let it sync to your outlook program. Then delete the email off of the email server, and see what happens on outlook. Does the email go away, or does it stay as a locally cached copy? Doing that will give you an idea of what happens to your mail if it gets deleted, does it stay or does it go...
Typically your viewing the emails that are on the server through Outlook UNLESS you move them off the IMAP server to your outlook client, and then they are erased off of the IMAP account and stored locally on the pc for archiving purposes. So essentially if your email ever got erased off of the server, then the email provider would have a backup of your inbox, and could restore your mail.
Edited by chrisd87, 23 May 2013 - 08:51 AM.