No. We would unquestionably have air superiority against DPRK. In fact, we would be dominant in all ways. In a straight fight, they wouldn't stand a chance, blink and you would miss them.
They do have South Korea outgunned in every way, including our troops in the DMZ, and given the small number of troops, it would only take them a few hours to reach Seoul, being only 30 miles from the border. Granted, it would hurt them dearly to cross US troops and technology, but they would be able to do so.
Then consider the sheer volume of artillery and ordinance pointed directly at Seoul, a city of 10 million people. Whether it is chemical, biological, or nuclear, you can bet they could easily launch it right into the heart of the city.
One thing one must always remember when dealing with DPRK is it is run by a certifiable nut job with a golden girls haircut and a HUGE inferiority complex. They are itching to scrap and would do so at the first sign of US aggression. Furthermore, they know their only chance against the US is to blitzkrieg their way through South Korea and Seoul and mix their troops among the what remains of the South Korean civilian citizenry. Given the time it would take the US to mobilize to defend the south, it is entirely possible they would succeed, and I believe we all know how difficult a land war in Korea can be, especially when the North is bolstered with the fanatical devotion and propaganda that they are.
Kim Jong Il just isn't the sort you play cowboy with. The little f%&ker and his minions that worship him as a GOD are just insane enough to unleash Hell the likes that have not been ever seen in modern history. There's little doubt that DPRK would be mopped up over time, but the costs would be dear.