If the South had had the sense to abolish slavery early in the war, it would likely have swayed public opinion overwhelmingly to the South’s favor both at home and abroad. Had the South succeeded in splitting off from the US, however, one wonders what the future would have held for the new Confederate States of America.
I think that the mechanization of cotton picking and processing was making the need for human labor obsolete. Very few of the Southerners owned slaves. To your question about what would have happened if the Southern states had successfully split off, I think it depends on how long it took to recover from the devastation and not suffering at the hands of the Reconstruction carpetbaggers who made matters even worse?
Here is an excellent summary of the issues from someone who was living through it:
http://freenorthcarolina.blogspot.com/2014/05/if-i-were-southerner-as-i-am-northerner.html