One thing to consider is that when Germany united in 1871, they would have had an eye for gaining influence in the Americas, would they have reached out to the CSA?
Maybe more likely they'd reach out to the USA. Germany was the most widely spoken language after English in the Northern states, and there were many more Germans there than in the South. The US shared a border with Canada, and British influence might have led the UK to favor the South on the theory that my neighbor's neighbor is more of a problem to him than to me. If the US actually were defeated, they might have found a friend in the new Germany.
Of course, if the South were damaged enough but still managed to win, they might be the one's to reach out to Germany. All the more so if the CSA tried to expand to other parts of the hemisphere. But if the US really were humiliated by defeat, Britain might favor the CSA, and the USA would draw closer to Germany.