Office 365 will not support a MAPI connection from Outlook 2003 since Public Folders are no longer available. For BPOS, this was possible because of the add-in developed to allow for Outlook 2003. Outlook 2003 requires Public Folders to be available
in order to connect to Exchange.
On the other hand, IMAP/POP should function normally if you choose to configure that. The configuration info will be in each user's OWA under Options in Office 365.