It's not an analysis, but simply an observation. BLOOD AND TREASURE rather solidly demonstrates the existence of the KGC as an episodic force on the border, mostly because it was a filibustering operation. While Frank Klement's DARK LANTERNS grossly overstates the case in denying the existence of the KGC, it is substantially correct in pointing out that there is virtually no evidence that it was any significant force in promoting Confederate war goals...and that the rumors of the KGC ultimately permitted a much more repressive policy on the part of Federal officials in the North.
It's interesting to run down the state recruiting officers of the KGC of 1860 to Civil War service. There are surprisingly few with any readily identifiable Confederate service...and those that are were hardly high-ranking officers or officials.
The more recent material I've read touching on the OAK indicates a much broader attempt by the Confederate authorities to establish something real behind Union lines. At some point, Richmond sent Emile Longuemere (various spellinhgs) and others behind Federal lines to do this. They tried, but, by every indication, were able to get very little out of it.