This Emperor was a young boy who ruled the Agatean Empire during Twoflower's visit to Ankh-Morpork. It is most likely that this is the same as the boy who is met in Mort. In Mort, someone is trying to poison him, but after a lengthy argument of who should eat the poisoned food, the boy Emperor forces the would-be assassin to eat it. The assassin dies, Mort collects his soul and goes on the way.
He is clearly dead by the events of Interesting Times, as there is an extremely old dying Emperor.