MS Exchange 2003 does not support Exchange Web Services (EWS), only Ex2007 or higher.
TMSXE 3.0 or higher requires EWS. So no, TMSXE 3.0 or 3.1 can not support Ex2003.
The older versions of TMSXE used software plug-in on Exchange server, which Exchange admin's did not like, and the integration was not as good as our EWS solution. This older version of TMSXE we have end of sale also, for the above reasons. Plus as you should know, Microsoft has end support for Ex2003 more then a year ago, which makes it difficult for us to continue to test and support.
We have not done any testing of TMS 14.x with TMSXE 2.x, and would not recommend. And TMSXE 2.x would not be supported for Webex endabled Telepresence integration.
Highly suggest you look at migration to Ex2007, which can support EWS and Webdev at same time if you have other applications dependent on EWS. Many benefits on the Exchange admin and scale and troubleshooing in doing this upgrade.
Sorry if not the answer you wanted to hear,
Ron Lewis
Cisco