From Brandon's signing tours we know that Alviarrin received the same mark as the other Forsaken/Chosen. We also know that there were originally more than 13 Forsaken/Chosen. I know Alviarrin hasn't the knowledge or one power strength of the original Forsaken, but in all other respects she is the same. She's been marked, after all. Anyway, I think she will live. She's smart enough not to show back up at the White Tower, so we probably won't see her again probably until Tarmon Gai'don. I think that Mazrim Taim has probably also received a special marking/power from the DO and he should be considered a Forsaken now, but I think he'll be killed by Logain.

I know you were asking about the original 13, so among those, I'd put my money on Demandred. He seems to be the smartest and his battle instincts are the best (see the Cleansing).