Yes. The software package that has caught my interest in particular (called w-agora) does this.
It's located at http://www.w-agora.net/ It looks like it does everything we need (All the features and advantages that you've mentioned, that I remember). I've set it up here to test it out, and it looks pretty good.
It runs on PHP/MySQL of course, and its customizable enough that we could do most anything we wanted with it.
Oh, and the messages are searchable too, without any external programs.
-Ryan Edgar
Created on Thursday, June 07, 2001 9:36 PM EDT by Ryan C Edgar