It all depends very, very much on how, why and when the armed conflict is avoided. I do not believe that the north would ever tolerate secession occurring without a fight. Keep in mind, despite what some people like to claim in a rosy-coloured image of history... the war was fought to preserve the Union. Not to free the slaves. Many people in the North would at that time prefer to end slavery, but few would have fought purely to end it. "Save the Union!" was the rallying cry. So even if the South had magically decided to free all slaves before seceding... there would have been war. The only way to prevent war is to prevent (or quickly undo) secession.
Now, I don't think that compromise at the eleventh hour is unthinkable, but it is a long shot. Remember that the Crittenden Compromise was rejected by Lincoln quite explictly. Less well-known (partially, I think, because people don't like to talk about Lincoln's less-than-perfect actions) is the fact that Lincoln in fact offered tacit support to the proposed Corwin Amendment... if that turned out to be a workable compromise. Lincoln's views certainly evolved over time, but before the war, he had been a bit of a period-typical racist: he did not believe in black equality, avidly supported ideas like mass deportation of all blacks to Africa (an idea he never mentioned again after the 1850s, but never actually renounced, either) and in the middle of the war, it was still his view that if he could preserve the Union by freeing no slaves at all, he would do it (even though he abhorred slavery). So, much as we may all despise slavery, it is not unrealistic to consider a scenario wherein Lincoln actually allows slavery to get constitutional guarantees, if this looks like the best and easiest way to preserve the Union and (permanently) end the threat of secessionism.
The key difference between the Crittenden Compromise and the Corwin Amendment was that the Crittenden Compromise would have extended the Missouri Compromise Line to the Pacific, making everything south of there slave soil (which ran counter to the Republican platform), whereas the Corwin Amendment aimed to protect slavery in states where it already existed, and guaranteed that Congress would not interfere with slavery without Southern consent. (The idea was also that this Amendment would be an eternal guarantee, I think, meaning it could never be altered thereafter in any way, including via another amendment.) Essentially, the Crittenden Compromise was unacceptable to Lincoln, and the Corwin Amendment was unacceptable to the Southern fire-eaters.
The Corwin Amendment had, however, already passed Congress before Lincoln came into office and was awaiting ratification by the states. Lincoln was also open to the possibility of a new Constitutional Convention to make further amendments to the Constitution. If either side had suffered a "loss of nerve" at this crucial stage, I think war could have been avoided still. A possible compromise would be for the South to forego demands that California become open to slavery (as under Crittenden) and to accept that only the Southern half of New Mexico Territory (corresponding to "Confederate Arizona") would become slave soil, along with Indian Territory. This would allow for limited future expansion of slavery, and a guarantee of its continued existence. If the Southern slavers had been sane, they would have accepted this at once. Personally, I think they would have rejected it. Because they were not being rational about the issue at all. But there is a chance they would have gone for the deal, and then... well. Lincoln's proposed new convention would certainly have been interesting, because his own aim in return for making slavery guaranteed was very obviously to make secession explicitly impossible. (And if an earlier deal had been reached, I think the South would not object to banning secession. there is a certain historical irony here, in the fact that Lost Causers like to claim that the South fought over secession, not slavery, while avid supporters of Lincoln like to claim the war was fought to free the slaves. The truth was reversed: it was almost entirely about slavery for the South, and almost exclusively about preserving the Union for the North!)
Anyway, that kind of compromise is a long shot. If it is reached, slavery will last for quite some time still. The exact nature of the compromise, however, does not mean that states' rights are going to be more of a thing. Just slavery. Lincoln will still be working to strengthen central authority, and history is working against the idea of states' rights. Also, regarding slavery: do keep in mind that this is not a "CSA wins"-scenario. The Confederate constitution made abolishing slavery more or less impossible. The Corwin Amendment "merely" means the states have to do it themselves. In the Deep South, this will mean slavery lasts for a long time. In the Upper South... I think not. I know, there are people on this board who like to argue that Upper South states had been "on the verge" for decades, and never actually went ahead with ending slavery. But keep in mind that cotton prices historically had an up-and-down cycle. By the early 1860s, cotton prices had been enjoying an all-time long "high" period, lasting several decades. Cotton prices were due for a crash. When that happens in this ATL, cotton (and slaves, since the southern slave economy had increasingly gone to 100% cotton plantations) would certainly become worth less. At that point, the abolition of slavery would become more realistic in certain states, at least.
Far more realistic than a last-ditch compromise, however, would be an earlier POD that leads to an earlier lasting compromise. This would work to remove tensions, so that secession would nver become a serious option. In that kind of scenario, the eventual end to slavery at a relatively early stage becomes even more realistic. The same economic factors apply, and because fighting a war over slavery is never even considered, the idea is slightly less militantly ingrained, I think. Consider the fact that every other Western nation managed to abolish slavery during the nineteenth century. Brazil did it in the 1880s. No other Western country needed a civil war to get it done, and none of them held on to slavery into the 20th century.
I think people who think the CSA, if independent, would have held tight to the institution are right. I think the people who think the USA would have done so in a "no civil war"-scenario are wrong. Especially if we are talking about a scenario with no secession and an early compromise. In such a scenario, slavery would have faded out, state by state in the Upper South, throughout the 1870s and 1880s. Eventually, in the late 1880s or early 1890s, only the Deep South would still have slavery, and at that point, it just becomes possible for the increasing number of free states to amend the constitution without Deep South consent and simply abolish slavery outright.