CS, first, I'm not familiar with TAS. Somehow I doubt it is "for all intents and purposes a TCAS system ", since tcas systems talk to each other, for example to ensure one will give a climb command, and the other will give a descend command.
So if a tcas is head to head with a TAS, I expect it to treat the Tas aircraft like any other non tcas transponder aircraft. That is, the tcas aircraft will get a climb or descent to avoid.
Incidentally, the tcas will know the other aircraft does not have a tcas, and so the climb or descent will be issued earlier than if the two aircraft were both tcas equipped.
Hawk