Frenzy: "How can Slayer know that Rand is his nephew?"
Jordan: "The Shadow knows a lot about Rand. They know a lot about Perrin and Mat too - once they began to identify possibilities, they went hyper trying to get information because anything might be part of the key to controlling him."

This rather indicates that the Shadow generally wants to control Rand, though in certain situations his death is ok (e.g. if he plans to Cleanse saidin).

Of course, RJ also said that "yes, the Champion of the Light has gone over in the past. This is a game you have to win every time. Or rather, that you can only lose once - you can stay in if you get a draw. Think of a tournament with single elimination. If you lose once, that's it. In the past, when the Champion of the Light has gone over to the Shadow, the result has been a draw."

So, just having the Champion of the Light on your side, doesn't mean that the Shadow will definitely win but just get a draw.

Finally, RJ also said:
"There are degrees of victory. The Dark One can achieve victory by breaking free, but can also achieve lesser victories. Such as by stopping the Dragon Reborn from doing other things he was born to do. It isn't as simple as him being born to fight The Dark One. It's never simple."

It's apparently really not that simple.