Would a Confederate States of America survive?
There can be no doubt hat the CSA would have survived to this day but in what condition? To build an economy through trade with Europe and the USA, slavery had to go. European investment would have developed the infrastructure needed for stability but the relationship with the USA would be the most important factor. Had independence been achieved without a war, friendly relations would have been achieved much sooner. Nasty war like the historical one would have created a deeper rift, which might have lasted through the First World War. I could a number of potential conflicts between the two nations, especially in the Central America and the Carribean. Europe would have done its best to promote division, especially Great Britain.
Assuming the common threat of the Nazi formed the historical alliance, the world would probably be a much better place. The USA wouldn't be the only super power and English speaking people would have another option for self-government. I am puzzled about one thing however; where do the northerners spend their winters and spring breaks and would the South ever have developed Major League Baseball.
Considering the dismal state of most of those states' economies today, it's likely that once the market for cotton diminished, they'd have found their standard of living severely curtailed and some agitation to rejoin the Union. Some, like Texas, might have discovered new wealth in oil, but without investment from Northern states it would have been hard to exploit it. Likewise, as cotton became more mechanized, unless the South were positioned to take advantage of it, their profit margins would have shrunk relative to others around the world who did mechanize.
Much depends on how interested the Northern investors would be in dealing with Southerners. A lot of Southern economic development in the past 151 years has been courtesy of Northern money.
The romantic answer would be ‘yes, absolutely!'. But I think the realistic answer would be ‘no'. I think once the issue of secession was settled, a ‘confederacy' once separated from the support of the Union, would fairly quickly fall into a chaos of infighting as each state insisted on its individual independance then began warring with other states over state lines and property rights and resources and arrable land and especially water sources. Then there will be all the separate groups and factions within each state warring over much the same issues. With no central governing body in state or as an over seeing government i think the ‘confederacy' would rapidly turn into a bunch of warring fiefdoms, many of which would be dictatorships and police states and/or theocratic oligarchies.