I do believe that there would have been a war again between the U.S. And C.S. states. First because the Northern States would not have been satisfied to let the southern states go free so easily. They would have been looking to almost any political excuse to retake the Confederate States and reunite all the former states back under the United States flag. Hence the excuse of the Western expansion. remember "preserving the Union" to maintain political power was the first "war cry" of the northern states.
Second, the Independence of the Southern States would not have settled the question of peaceable secession of States from the Union. California, Oregon, Washington, Colorado, Kansas and Nebraska were very pro-union during the War and would not, I believe, have joined later with the Confederacy. The territories of Arizona and New Mexico, which were Confederate, would have been the "flash point". Just exactly where would their Northern Borders be? Southern California would have especially felt threatend by Arizona. I believe that this would have been the political trigger to again start another War between the U.S. and the Confederacy.
I would point out history and the Spanish American War, and "Remember the Maine", as an example of this attitude of manifest destiny and how such a war would have been started. There would have been some incident of territoriality that would have sparked such a war.