I disagree with many on this forum from the Northern perspective. I believe it would have died out on it's own within 50 years or so. The parallel demise of the institution in the Americas bears this out in my view. We'll never know. What we do know is that Jeff Davis and others in America were attempting as late as the 1850s to expand slavery not only across the rest of the North American continent, but also south into Cuba.
Cuban slavery ended in 1888 I think more or less. You are right we will never know but if one takes the position that slavery would have continued in the American South then what would one say of the way in which it died everywhere else. Or would one say it died everywhere else because the South did lose. I'm not sure. No doubt the defeat of the South certainly must have had a psychological effect on other societies in the Americas where slaves existed but many other factors also contributed. The English abolition of slavery and their slave ships which were far and away the largest flagged fleet in the trade was arguably as great an event in the abolition of slavery as the "war". Society and political systems and industry and demographics (Brasil and SA especially)and yes...even humanist thought all contributed to the demise of chattel slavery.
Of course other forms of far worse slavery was practiced by the state in various totalitarian states in the 20th century and is even now practiced in chattel form on the very continent from which the trade in question originated. The book is not yet closed. I feel for sure that we have not seen the last of state slavery in totalitarian regimes for a long time to come.