Depends on what you mean by "the South". If you mean a majority in the Confederate Congress elected in 1863, it would be difficult to argue otherwise. But, if you mean the rank and file Southern soldier or citizen, from Robert E. Lee to common people in the towns and countryside, the answer points towards independence.

The best resource on this issue, which like most issues can be argued either way, is Robert F. Durden's ground-breaking study, The Gray and the Black: The Confederate Debate on Emancipation. Here are several reviews --
http://www.amazon.com/Gray-Black-Confederate-Debate-Emancipation/product-reviews/0807125571

As I've mentioned many times, period newspapers make excellent historical sources. Prof. Durden uses newspapers frequently, including articles, letters and petitions found in them. A petition which impressed me was signed by nearly every officer and enlisted man of the 15th Alabama Regiment, a command I have studied in some detail. They urged Congress to advance the legislation before it. Since typical Southern boys daily worked alongside black people in the fields and towns, they readily accepted the idea of fighting together in the ranks.