Although it is true that a war is not expedient to the recession, the long-term economic benefits of a defeated North Korea and and a united Korea most certainly are beneficial.
Beneficial to the United States, but not to China.
http://www.nytimes.com/2010/11/24/world/asia/24beijing.html
“At the moment China has limited influence,” said Cai Jian, a professor of Korean studies at Fudan University. “On one hand it’s unhappy with North Korean actions and its provocative behavior, but on the other hand it still has to support North Korea.”
The support continues because China fears that the vacuum created by a sudden collapse there would open the door to rule by South Korea, “and that will put an American military alliance on the doorstep of China.”
...
“No matter whether it be within the party, among the people, or even within the military, China has grown increasingly sick and tired of North Korea’s rogue politics,” said a senior Chinese media commentator, who asked not to be named because of the delicacy of the issue. “But strategically, China’s kidnapped by it.”
China is the biggest energy consumer and rising economic power. So speaking of long-term economic benefits, what's good for China is good for the global economy.