If you back up the OST file (via drag and drop to a hard drive or via batch file or similar), using 3rd party tools you can turn this into a PST later if you need to access it. There is no direct way that I know of to have Outlook open an OST file. What you also have to watch is that Outlook 2013 only caches the last 12 months locally in the OST file. If this is unacceptable to you, then you'll need to adjust this in the account properties.
CloudAlly anbd CloudFinder have online daily mailbox backup options for US$3/month. Never used them so you would have to look at things like retention periods (how long you have got to recover a previously deleted email).
Backing up your Cloud services = smart IMHO. Hopefully like insurance it is a waste of time, but providers do lose data from time to time and Microsoft are not immune.
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