No, as the Outlook client stores the Hosted Exchange email in a *.OST file, the Cloud Backup software will automatically skip this file.

OST files store a cached version of your mailbox that resides on the Hosted Exchange server. When your device is not connected to the internet your Outlook client will displayed the cached content stored in the OST file and will immediately update when connection is made to the server. As the Hosted Exchange server is the primary data location, the Cloud Backup software will not backup the *.OST file.

The Cloud Backup software will only back *.PST files which are local mail storage files that Outlook uses typically for POP / IMAP based email and archives.