I imagine IMAP would provide access to most cloud-based email services, and I bet there are some IMAP-based export tools. However, in my experience, Microsoft Exchange email accounts are only accessible through the Exchange Server protocol, whatever that might be. Outlook is the perfect intermediary.
The server that provides access to Exchange through Web Access can also provide for IMAP.
However, as there now is native support for ActiveSync in most operating systems there no longer is a very compelling use case to turn it on and run the associated risks.