Yes, but probably not from nuclear weapons. Two crude, untested nuclear weapons constructed by the best scientific minds in North Korea (*snicker*) may not be the primary casualty causing devices of this particular fight.
A war on the Korean peninsula would be a bloodbath, no doubt about it. The outcome, however, is not in doubt. They'll put up a great fight for the first two rounds, then collapse. (Surviving the first two rounds probably isn't in the cards for most of the U.S. forces in the initial fight. This victory will come at a steep price, by any reckoning.)
I don't know exactly what prompted that parenthetical "snicker", but I spent a lot of time in Korea, and the Koreans do have lots of very good scientists and engineers. The average Korean High School graduate probably knows more math and science than 90% of American college graduates.
I'm not a big fan of the North Korean government, but the people are not stupid (although they are kept uninformed about outside events).