I don't know the answer to the title question. I know that with all the talk about the DPRK launching artillery into Seoul, South Korea upon the advent of war with the U.S., either the C-RAM systems are either not as effective as it seems they would be given
the U.S. military's description of the system, or South Korea doesn't have the system implemented even if U.S. forces deployed there do.
Even if it's there and fully operational NK has tens of thousands of artillary pointed at Seoul, 1.1 million troops and 5,000 tanks ready to roll thru the DMZ. About a thousand aircraft many of them that can carry their nukes. Yeah, shoot them down now you've got nuclear material scattered all over. Then you've got the moles. Probably tens of thousands in SK posing as locals who'll conduct behind the lines mayhem.
NK will cease to exist, but the first month of war will be ugly on a scale not seen before.