Yes, I was. The men who enlisted in 1861 were not forced to remain in the army after their 3 years were up. Well more than half did choose to reenlist, even after three hard years of fighting, a figure comparable to current US Army reenlistment rates . A draft was established in 1863, but less then ten percent of US Army soldiers were draftees (or subsitutes). Men who had served as enlistees and been released at the end of their three years were not subject to the draft. Some did become paid substitutes for other draftees.
But since you're attributing enlistments, reenlistments and draft rates with support for war aims and policies what do you have to say about the confederacy's refusal to let to its men go home after their enlistments were up, unilaterally extending them indefinitely, the fact that the south went to a draft earlier, that conscripts made up a far larger portion of the southern army than the US Army, and that desertion rates were much higher?