First off, i doubt that their missles are deployed near the DMZ, but you still bring up a valid point.
The North Korean communications system is primitive, they throw nothing away. They still have T-34 tanks! The South Korean commo systems are modern and probably shielded against EMP. At any rate their military net is, and that is what is important. The entire DPRK would be taken down, except for old vacuum tube units, which are immune to EMP, but must communicate in the open.
With their command and control crippled, the DPRK isn't going to be in a position to fight anyone, or to launch anything, though i still wouldn't want to be the ground commander with orders to invade the DPRK, that could be a little intense.
I doubt if all the civilian stuff is.