Not usually, there are good political reasons why war is unlikely.
But it's worried me before--I mean, good intelligence on NK is hard to come by, and they are a power-hungry totalitarian regime with a malnourished population and absolutely no value or significance on a global scale except as a potential nuclear threat. I was concerned when Kim Jong-Il died, but nothing really happened. I was definitely concerned during the November 2012 bombings on the island near Incheon, but again, the situation was diffused by South Korea. I remember that the Wikileaks that came out around that time revealed China is more annoyed with North Korea's bomb-happy temper tantrums than many thought, and I feel like it's a sound analysis to say they wouldn't back NK in a full-fledged war.
All that to say I understand your question and I don't think it's wise to be totally blase about the situation or ever forget that South Korea is a country still technically at war with a very unpredictable and not exactly powerful but very armed enemy to the north. It's probably good to have some kind of plan in mind for what you'd do if something were to happen and evacuation was necessary--having the means to get yourself out of the country, having a place back home you could crash last-minute if you had to, etc. I know that if the U.S. Embassy ordered Americans out of the country, I'd be gone, it's not worth the risk to me. Something everyone moving here must evaluate for themselves.
