re: Had the South won would New Orleans be the largest/most populated city in the US?

Hard to say, but I'm inclined to think that most states would have returned to the USA after a few decades. The core coastal states may have stayed together as a confederacy, but as for the other states that joined after Fort Sumter, that was mostly just solidarity with their fraternal Southern states and not wanting to be forced by the USA to go to war against them.

People think confederalism is unstable, and it sorta is, but the loosely aligned medieval German principalities of the Holy Roman Empire lasted for centuries. Then again, an international moral campaign would surely have been waged by Anglo-American civilization against LA, MS, AL, GA, & SC. It would probably have become the 19th century version of South Africa and Southern Rhodesia. Eventually, I think all 11 states would have returned to the USA after 3-4 decades. Moreover, it would be a USA that would not be as centralized as the one we have today, because the 14th Amendment would not have passed the way it did in reality.