If I understand correctly, an auto-afk function would be enabled by a server-side script. From searching the TS forums I came across an addon called TS2PerlMod which, among other things, "Moves idle users into a channel of your choice. The channel can be specified by a full or partial name." This sounds like just the ticket for fixing this problem. Whoever is in charge of running the TS server should check out the file
here.
I also came across some other addons for TS users.
Teamspeaker adds a bunch of features for the client including an option to auto login to servers of your choice.
TS Overlay says it can overlay text of who is talking overtop of a game. So when you are in-game it would say "Kolath is talking" whenever I have my mic active. I haven't tested it out yet, but it sounds useful.