According to this guy, North Korea possibly could:

Most military strategists agree that cyber attacks are an excellent first strike weapon. In these specific circumstances, cyber attacks might be considered by Pyongyang as an appropriate and proportional response to the U.N. Security Council’s condemnation and reinforcement of existing sanctions. High probability targets if DPRK launches cyber attacks include South Korea and the fifteen countries that make up the current U.N. Security Council that include — permanent members-China, France, Russian Federation, the United Kingdom and the United States — and ten non-permanent members Austria, Japan, Uganda, Burkina Faso, Libyan Arab Jamahiriya, Vietnam, Costa Rica, Mexico, Croatia and Turkey. This calls for increased vigilance by cyber security professionals guarding the critical infrastructure of those targets identified above.

North Korean Cyber Capabilities Estimate:

Unit: 121

Established: 1998

Force Size: 12,000 declining

Cyber Budget: $56+ million.

Goal: To increase their military standing by advancing their asymmetric and cyber warfare capabilities.

Experience: Hacked into South Korea and caused substantial damage; hacked into the U.S. Defense Department Systems.

Threat Rating: North Korea is ranked 8th on the cyber capabilities threat matrix developed in August 2007 and updated February 2009. [Defense Industry Daily]