He actually has nothing to do with anyone in the story. Troll Alpha Complex is an underground city/bunker that was built in anticipation of Sgrub, designed to survive a meteor apocalypse. But, as is custom in Paranoia, someone betrayed the others, brought a copy of Sgrub underground, and installed it in an attempt to ensure Troll Alpha Complex's destruction. Probably because his secret society wants to destroy the world or wipe out the trolls or something.

Anyway, DT comes into the story either as the meteor's approaching, if I want to include a whole assload of NPCs, and the story follows him for a little while as he hunts down the traitor, or slightly after most of this went down, after DT's executed the traitor and the rest of his team is dead. Probably the latter. Either way, once we get to that point, I'll send out a distress call and try to get Troll Alpha Complex into the medium as a last-ditch survival effort.