The Norks could probably for the first day or so, devastate the front lines with an artillery barrage. Expect heavy civilian casualties and major casualties among front line units. Once US Air Power gets involved and starts crippling their communication lines, logistics, and ability to move, which admittedly isn't that great to start (they are still mostly using surplus ChiComm gear from the Cold War), they will start unraveling. Unless China really does have that NeoMaoist revolution people keep talking about, the Norks are on their own, and they will quickly find that feeding and supplying troops is going to be impossible (not that they do a good job of it anyways) once their infrastructure, which is really quite lousy, is caput. Expect millions of refugees going both North over the Yalu and South trying to brave the DMZ, with hundreds of thousands of deserting soldiers in the mix. An invasion of the North, due to the sheer depth of forces the Kim regime can line up, won't be a total cakewalk a la Baghdad 2003, but it would be pretty close as the North collapses.
How do you think the Chinese would feel if Kim died and someone outside the Kim family was chosen? Personally I think the Chinese would be happy they wouldn't have to be linked with someone so embarrassing.