A: YES, That was the purpose of seceeding in the first place to form an independent self governing country more closely attuned to the will of the Southern people.
Q; "as foreign to the USA (with the exception of shared borders) as any European country was then?"
A: NO, A shared culture, economic trade and common interest of the people, would have kept the people far closer than those of Europe. Politics are another matter, that would have been the defining issue of seperation.
Q: "or might the South's realization of CSA "nationhood" have been at least delayed indefinitely, if not abandoned completley - based on the condition of the South's finances, infrastructure, etc. following such a CSA victory?"
A; This question has to be divided into two periods.
Most of the destruction in the south which you imply would have to be rebuilt occurred after 1863 at which point practical hope of independence was gone. If we are only talking here of conditions prior to 1863, in which the destruction to civilian inferstructure was minimal, had the South gained it independence prior to July 1863, before the wanton destruction of the interior states occurred in 1864 and '65, the South had a reasonable chance of forming a new nation. The South would have transformed fairly rapidly from strickly agricultrual interests to bring in more industry to compete with the northern industrial might after the war.
Had peace and independence transpired after 1863 there was a good possibility that the Confederate States would have formed an allience with one of the European countries, probably France, for its protection. This was, according to a report made in late April 1865, contained in the O.R.'s, part of the reason that Jefferson Davis was attempting to move the Confederate Government to the Trans Mississippi Dept. in April 1865, in order to join with the French Governmment of Mexico to become a french provience and under Maximillian's protections. Maximillian was very receptive to this because of Lincoln's attempt to get Santa Anna to leave his exile in Cuba in 1864 to lead an overthrow of the Maximillian Government. This is supposedly the reason why so many Confederate generals of the Trans Mississippi went to Mexico as the war was ending, in order to maybe return.
Q: "Had the CSA actually come into existence as inferred above, do you believe the CSA would exist today?"
A: Difficult to say. The Confederate States of America would not have collapsed on it own, but may have due to external forces.
Yes, there would have been changes internally, slavery would have ended because of economic reasons and would have followed the practise of the northern industrialist use of cheap labor, but not as slave labor. But, the general practise of a Republic form of Government would have meant that the decision making process at a national level would have been slow and pains taking, as that process was intended to be under the Constitution, more so than that of the more centralized United States Government after 1865. This would have put the Confederate States at a political disadvantage against the United States.
Also the question of westward expansion would have probably lead to a second war between the United States and Confederate States by the turn of the century. But had the Confederate States survived to the 20th Century they would have probably become one of the United States strongest partners, both economically and politically. It would have also put a check and balance to the politics of the United States.