In Outlook 2010 there was an option to have the delete action move the e-mails into a specific IMAP folder instead of moving them to trash. That option is apparently has been dropped in Outlook 2013.
When I delete an e-mail in Outlook 2013, it ends up in the trash folder on GMail. I prefer to just archive the e-mails in another folder/label and keep them forever or until I hit my 10 GB limit (which ever comes first :)).
My GMail IMAP settings are:
When I mark a message in IMAP as deleted: Auto-Expunge on - Immediately update the server.
When a message is marked as deleted and expunged from the last visible IMAP folder: Archive the message (default)
I would have thought that with these settings it would be impossible for an IMAP client to trash an e-mail.