South Korea would definitely not approve since this is the era of the Sunshine Policy; Presidents Kim Dae-jung and Roh Moo-hyun were both advocates of overtures to the North. Even if a conservative president took power I doubt they would approve of an invasion for the fact that, as stated before, it would be extremely destructive to the South even if reunification is achieved. Even a peaceful reunification would cause massive economic pain for the South. It's just mutually-assured destruction. Obviously, if the North struck first, then South Korea would approve, but there's not much reason for the North to attack during the peak of Inter-Korean relations.
I don't see any scenario where the US could attack the North independent of South Korea and not invite anti-American resentment for A. inviting war and destruction to their shores without any kind of approval, and B. sticking them with the costs of reconstruction of not only regions along the DMZ (including Seoul) but also that of the North when only relatively recently they had just recovered from an economic crisis.
I don't see any scenario where the US could attack the North independent of South Korea and not invite anti-American resentment for A. inviting war and destruction to their shores without any kind of approval, and B. sticking them with the costs of reconstruction of not only regions along the DMZ (including Seoul) but also that of the North when only relatively recently they had just recovered from an economic crisis.