Would the U.S. and the confederacy ever have allied together with anyone? You assume friendly relations between the two countries and I doubt that would have happened. Look at the revolution. Relations between the U.S and the U.K were strained through most of the 19th century. Confederate independence won through war would have led to an armed border, large armies and navies and probably more wars down the road. Alliances. Its more likely one side side would have allied with the British and the other side would ally with the French or Germans or anyone else as an offset.
As for what it would be like considering the precedent set by Davis in conscription, income taxes, forced government levies on agricultural products and slave labor I doubt that it would have wound up the small government, low tax paradise you imagine.