Yup. In fact, some argue they are better suited for it than we are:
They've probably done their own tweaks to the system hardware and software on the Patriots and SM-3.
Given the threat and activity, we've got eyes on the areas of known missile activity. Some of the NK missiles are mobile, but they still have to be launched from prepped sites. They can't be fired off on any old dirt road.
Within two minutes of launch, we have the trajectory, impact area, and firing solution plotted. While we are watching them, other interested parties like Russia and China are watching us. There is no reason to give away valuable technical data, unless the incoming missile is a true threat.
A successful intercept probability is increased with the presence of our Aegis ships with SM-6 and SM-3, their ships with SM-3, and their land based PAC-3s. If the North Koreans decided to launch at Guam, they would have to run that gauntlet, then get through THAAD based on Guam.