I don't think it would have lasted long enough to. A nation founded in blood and fire upon the proposition that its constituent territories can leave at will would likely have balkanized into mini nation-states in a generation or two.
That's a good point that I overlooked. Contrary to the unhistorical myths associated with confederate nostalgia, there was no unified southern nation. The rebellion was a political power grab by the slaveowning elite temporarily fueled by a burst of strong, but false and shallow, regional fervor. The idea of "southern nationhood" had no staying power in war and there's no reason to believe that it would have endured long in peace either.