That depends on if South Korea isn't able to take them out in first strike.

South Korea could take out the first barrage of NK's missiles and nukes with its THAAD system. After that it will be vulnerable. So SK's success in any future conflict is contingent on a successful counter to them, as well as a successful counter-attack that's able to take out all NK missile silos and artillery systems (a combination of drones and air force could do this). But of course, too many variables and South Korea would do better to not take its chances in finding out, and preemptively urging for peace.