I rather doubt that. The NK soldiers are three generations into the most comprehensive national brain-washing ever attempted. If they cross the border at all, they'll do it in a human wave attack.
I've no doubt whatsoever that they'd eventually fall apart, but not before they (and their artillery) make a huge mess in a significant portion of South Korea.
I agree, it will be bloody. The NK soldiers will come over in waves because they will have machine guns at their backs. I would think as soon as they are out of the line of fire, they will surrender in droves.
I just wonder how they would sustain any effort for a period of time.