no, since the CSA was a separate nation, they were uniformed combatants. Strangely enough, G Gordon Liddy says that it really wasn’t a Civil War since the CSA was a separate nation.
The CSA were separatists with de facto control over part of the territory they claimed, but were certainly not an independent nation. The rebels were not recognized by the US Government nor were they by any foreign state. The purpose of their rebellion was to create an independent state, but the rebellion was defeated.