Brown was attacking in the wrong places.
Instead of having a whole mess of men in one place shooting people what he should have done was sent them around to different towns and then had them all sneak out and torch the local cotton fields on a predetermined day (the coordination of the times would be circumvent the widespread security increases that would no doubt come about if they set the fires one at a time)
At best, Brown would have only precipitated a genocide. Remember, even in the North, abolition - much less civil rights - was a minority position that was not supported by the general population. The movie 'Lincoln' captures this ambiguity clearly at several points, with the common man voicing the primary concern that a free black man would simply be a competitor for the limited resources available to them. Neither the Northern nor the Southern working class was in the majority interested in freeing the slaves (or for that matter fighting to maintain the slave system). That's why for the most part the politicians on both sides of the war did not try to sell the war to the public as a war about slavery. Asking either the north or the south to fight a war for the sake of freeing or enslaving the black slaves was pretty much a non-starter. Both sides appealed to patriotism and economic self-interest. Swathes of the south where this economic self-interest was far from obvious de facto succeeded from the Confederacy and did their best to stay out of the war entirely.
But anything like a locally successful slave revolt would have changed the calculus in a hurry. A general uprising by slaves where non-slave owners were caught up in the slaughter would have hardened almost everyone - including most of the moderate abolitionists - against the cause. Faced with the threat of violence where the economic advantages of keeping slaves were overshadowed by the damage involved, the slave owners wouldn't have pursued an agenda of liberating the slaves, but would have in the majority likely have adopted the more genocidal practices seen in places like the Middle East or Brazil or in the Congo. It's an ugly thing to say, but the main thing keeping slaves alive and healthy in the US was the high economic value that they had. With importation of slaves illegal and slaves perceived as being valuable, murder of the slaves simply was bad business.
In a slave revolt situation, it certainly would have happened. In fact, it absolutely did happen. In the wake of Nat Turner's rebellion, hundreds of blacks completely unrelated to the rebellion and often at great remove of it were murdered under flimsy pretenses. Any larger revolt would have had certainly had an proportionately more massive response. The thing about people is that they do not think clearly when they are scared or angry, and general violence tends to be met with general escalating violence. Any sort of terrorist campaign to free slaves would have simply been met with corresponding ruthlessness, and there would have been protests but in the midst of the fear and the moral muddle of the situation, there probably wouldn't have been more than hand wringing.
The war was absolutely avoidable. From the time of the countries founding, there was a general consensus that slavery had to be eventually abolished. The trouble was always that whenever the question was considered, the immediate costs of doing so always seemed too high. It was always easier to do nothing than to say, "OK, now is the point we'll write the value of our human livestock off our ledgers." And even those that were willing to do that, never had a good answer for what the newly freed slaves would now do with no education, no capital, no land, and virtually no possessions. No one North or South no matter how disturbed they were by slavery had a good answer for where that money would come from. It couldn't come from the poor, and honestly there wasn't enough wealth even in the wealthy to pay for it even if they were inclined to do so - which almost none of them were. So they dithered, because all the compromises that might seen it done were ugly ones that made no one happy. People had forgotten that the nature of a real good compromise is that no one gets what they want, because the nature of a compromise is always that there is no perfect restoration to existing imperfections.
There were small scale answers that were adopted individually as some slave owners shared their wealth better and started converting slaves slowly to something like employees who could be set free. But that solution depended solely on human kindness and reasonableness, which are sadly things you can never rely on. The real answer to the question was to be found in automation and industrialization, which would add the wealth needed and eliminate the need for the manual labor. The war simply forced the question, and then the slow process of free industry in an increasingly prosperous world gradually put the black community on an economic footing that it could demand and receive their due political rights.
But, had the process been forced by violence and terrorism, the likely result would have been the adoption of automation and just killing rather than freeing the slaves. The ugly truth is that like breeds like. If you do evil even in a good cause, you just get more evil. Only good can drive back evil, which is why were were fortunate to have leaders that realized that.