Does Exchange Server integrate with Windows Server 2003's Windows Rights Management (WRM) component?

No. All of Outlook's Information Rights Management (IRM) features depend on the presence of a WRM server, but Outlook doesn't care where the messages are stored. In this respect, WRM is similar to Secure MIME (S/MIME): The sending client protects the message contents before submitting the message to the server for delivery, and the message contents remain protected when the receiving server receives and delivers the message to the recipient's mailbox.