I think the question is less about how accurate the North Korean missiles and nukes are, but rather whether they launch them in the first place. Nukes, and large quantities of missiles exploding on foreign soil is a statement enough, even if they do little damage to the opposing military. The impact, and even their launch, would be extremely damaging to the North's opponents domestically. Besides, a nuke does not need to be accurate to do what they do. If a nuke was shot down almost anywhere over the Straits of Japan, the radiation and blast would affect the Japanese and the South Koreans as well. Observe the effects of Chernobyl.
It also does not require a high level of technology to toss missiles over their Straits of Japan or over the 38th parallel. As Vekseid said, the sheer quantity of missiles would overload a missile shield.
However, I sincerely doubt that North Korea will really go ballistic. The use of the nuclear bargaining chip is a useful method to obtain aid and money from the international community, and the North is now posturing and saber rattling in a bid to regain attention. Even Kim and his generals, addled as they are, know that they cannot defeat an international response, and it is far more profitable for them to use their nukes as a way of dragging out more carrots from the international community.