Lysander Spooner's thought on the Civil War is popular among many libertarians even today. He's a pretty good approximation of what you would get if you plopped a hardcore modern libertarian into the Civil War period. He was a staunch abolitionist who wanted all the slaves freed immediately, but thought that the Confederacy was legal and that the Civil War was illegal. I'm not sure that he fits on either side of the war. So, to answer the question: No.
Auberon Herbert was also contemporary to the Civil War. He said: "I am very glad that slavery is done away with, but I think the manner is very bad and wrong."
How is this not clear? If you think that the Confederacy was legal and thought the Civil War (action of North against the South as many Libertarians/Dixie lovers believe) was "illegal" then you supported the South in the Civil War as well as it's institutional slavery. That's not a confusing concept.
The best argument against modern day "libertarians" is how they would have reacted in historical situations, with the Civil War and Civil Rights being major demonstrations of the shortcomings of the ideology.