Short answer: Yes. It would be an absolute bloodbath, no two ways about it, but the North doesn't have the edge to get the job done. They have a variety of tools at their disposal, but the bottom line is that the South has been preparing for this for 50 years, and they know where to expect the mischief.
After the first week, the North will have either taken Seoul, or be facing a massive mobilization and counterattack. Within two to three weeks, most of the invaders will be on the run (or have deserted en masse), and the North will be done for. Even if Seoul falls, the North won't be able to hold it for long.
The North has some fatal weaknesses that will be their undoing. They have the most inflexible chain of command on Earth. They would have no way to exploit battlefield opportunites crucial in an invasion, because of their command structure. The South, on the other hand, is deadly, agile, and wired.
Also, the KPA is expected by both sides to be reliable only in garrison. Once the troops are out from under the secret police, and moving South, they will see for their own eyes wealth they've never dreamed of. Entire units will simply vanish. The higher ranking officers, who by necessity know what to expect, may become unreliable if ordered to move south into certain defeat.
All in all, war would be devastating for the South, but fatal for the North.