Aren't you assuming here, that the CSA will be a North Korea-style isolationalist entity, foregoing trade and contact with outsiders, and with no attempts at diplomacy?
I mean...we all thank our lucky stars that the Union won, but whenever I come across: "Oh, the CSA would just have collapsed soon after, and then it'd have been the same result as now, and we'd all live happily ever after", I immediately become sceptical. Lots of countries rose from seemingly impossible odds. Despite been deeply racist, the leaders of the CSA weren't imbiciles.
The south's main trade product ( and one might say only product in it) was cotton, which by the time of the Civil war was being effectively sidelined by Cotton from France's and England's colonies.
Given the heavy conservative nature at that time and the way the South office holders and men of political nature went about their work its very unlikely that the South would be in such a rush to switch to different trade products.
And even if they did its hard to think that any trading Nations would want to do business with a slave holding nation and since the South is a Trading and Agriculture based economy it would be devastating economically.
The very widely held view that the CSA wouldn't be able to function or stand alone on its own hold much of it to the massive and heavy fissures that formed during the Civil War.
Governess wanting to keep their troops in their owns states, whilst at the same time wanting more troops from other states insisting their states were more important than any other.
The East and West fronts are living proof of that, the Confederacy in the West was a complete mess of political officers who had no idea what they were doing (Polk being the biggest example) and kept in their positions by Davis because their individual states wanted them their thus hurting what ever chances the CSA had in the war.
Not to mentation how the CSA west was basically sacrificed for the East, the massive political problems that the Richmond encountered and only grew more and more larger as the war went on adequately demonstrated just how the CSA form of government was unworkable and would snap given the right amount of pressure.
The stubborn defense of Southern arms are the only reason why it managed to hold up for so long.
Given all that it really stretches the thinkable when one thinks of the CSA able to properly function in peace time, let alone being able to advance economically, politically and socially.
And yes Nations like men have beaten the odds before but in this scenario and from what we have seen of the CSAs Political order when confronting issues during the Civil War i heavily doubt the CSA could survive.