If you have a local PST file and open it, will it "mirror" either to Outlook.com or another installation of Office 2013, given sufficient time to upload.
Or would you have to kluge it, perhaps by making a bunch of folders in the "email folder" or something? The Office 365 I got has 1TB cloud storage so large PST files shouldn't be an issue...unless it actually deletes and downloads the whole thing each time you log on or something I guess.