It's impossible to say how long slavery would have survived in the Deep Cotton South, had there been no Civil War.
But we know for certain secessionist leaders in 1861 gave protecting slavery as their main reason for declaring separation.
And as late as early 1865 they still refused to consider compensated emancipation.
So it's impossible to think that generation would ever consider abolition & full citizenship for slaves.
Indeed, their descendants refused to grant full citizenship until forced by Federal government to do so.
So there's nothing to suggest that Deep South slavery was headed for early or peaceful extinction in 1860.
By 1860? No. By 1900? Maybe/probably. Brazil was the last in the West to do abolish it and that was in 1888 and without a war.