If the South had won the war would it have ended slavery?
No.
I have no idea when or how slavery would have ended had the South won. It’s an interesting counter-factual, as there would have been further wars over western expansion and extensions of slavery. For this thread, though, the question is if Lincoln had overseen Reconstruction, would things have been different for blacks?
What we can know is that segregation and economic isolation were imposed upon the former slaves immediately after the Civil War, even with the presence of Northern armies for another 10 years. The armies were going to be there for a time, regardless of Federal policy, so it’s a matter of the extent to which Reconstruction succeeded in its purposes.
What progressive historians like Foner miss is that Reconstruction’s primary purpose of reunification was a complete success. By 1877, the South was politically re-integrated into the nation. From my general research on the early 1900s, I can attest that upon the 50th anniversary of the end of the Civil War, the lasting memory of it was of a war well-fought and a Union retained along with sectional good will. That was Lincoln’s primary goal. But what is less apparent is if the reintegration had to follow the path it took, namely Republican rule with black legislators enforced by the Army, and if Lincoln would have supported these methods.
Reconstruction’s secondary project, citizenship for the former slaves was also a success, despite the ongoing political suppression of blacks. Citizenship, equal protection, and suffrage for blacks were the South’s cost of losing the war, so I doubt Lincoln would have opposed the 14th and 15th Amendments.
But Reconstruction’s tertiary project, civil rights was a mess. Lincoln surely would have known that it was counter-productive to impose Republican local rule in the South with black officials. I also doubt he would have required adoption of the 13th amendment as a condition for readmission (as Grant did)— it was already adopted nationally. Congress and the Federal government had plenty of opportunities to pursue reasonable protections of blacks (such as the 2nd Morrell Act, which gave financial incentives to create black land grant colleges) without unrealistically trying to force them upon Southern whites. The fuller Reconstruction program required the Army, which led to more Southern resentment, more reprisals against blacks, and more general exhaustion over the entire program. By the time the 1875 Civil Rights Act was passed, there was no realistic hope of enforcing it (Grant did not), so it was just posturing and provocation, which only led to its nullification by the Supreme Court.
To sum up, I suppose what I’m arguing is that Lincoln would have allowed for a kind of salutary neglect (within the baselines of the 13th, 14th, and 15th amendments), which ultimately would have yielded better race relations in the South and better outcomes for blacks than what followed Reconstruction’s imposed political and racial agenda. Salutary neglect worked in the North, which also exercised de facto and, in many places, de jure segregation, yet the black economy exploded. By 1909, American blacks were, as an aggregate, already the wealthiest group of blacks in the world - merely 40 or so years after the end of slavery. And that was not because of Reconstruction, it was despite it. I think we can clearly attribute fifty years of legal segregation to Reconstruction, and not to its not having gone far enough, as leftist historians argue.