The biggest fallout of "killing an Ascian" is not if the Ascian is actually dead. It's that they are not in whatever host they possessed and can no longer manipulate a situation from that host. The most damage the Ascians managed to do against the Scions stems from the fact that the Scions had no reason not to trust Thancred with all their information. The odds of them manipulating situations elsewhere from possessed hosts no one knows are Ascians is very high (Suishi of the Violet Tides is a good example). The big problem is, so far we've never seen anyone figure out how to tell if people are actually possessed by Ascians... but you'd probably need to be able to do that if you're specifically hunting Ascians...