Well, heck...
I went and read the Wikipedia summary, and apparently the plan, had it succeeded, was basically for a lot of slaves to free themselves by killing their masters (and I hardly think that is outrageous) and then immediately flee to Haiti from Charleston.
So, had all gone according to plan, the impact would have been hardly worse for the slaves of the South than it was OTL, at least some slaves would be freed but they'd immediately remove themselves from mainland North America. Consequences might be bad for Haiti if the USA mobilized to attack, with the island nation giving the fugitives refuge as the excuse, but then again I think an American invasion of Haiti would have become a Vietnamesque quagmire (as it had for the French), which is presumably why the US held off from trying it until our imperialistic period well after the Civil War.
For American slaves who did not escape in the plot, things would be bad as the white government cracked down hysterically. But that's pretty much what did happen OTL anyway. With the example of a successful revolt before them, perhaps there would have been more insurrections, and I say goody. Perhaps the whole question of whether slavery is really something the United States should have at all would be revisited with more force, even in the South, where profits would be weighed more exactly against the danger of getting murdered one fine night. Again, good.
Frankly I'm kind of disappointed, I always figured plots like Vessey's were aimed at trying to establish themselves in permanent residence here in the USA as some kind of maroon republic bastion. Which possibility is ridiculed and possibly ridiculous, but then again in some regions of the South the slaves outnumbered the whites, and the assumption they'd surely be put down relies on the Union as a whole acting to quell them. Which is clearly something the framers of the Constitution had in mind, but the possibility exists of the ex-slaves fighting their attackers off well enough to secure some kind of negotiated truce, allowing them restricted territory the Union doesn't intrude into, and the eventual prospect of the self-liberated zone re-integrating into the Union having set the precedent that African-Americans are indeed free Americans too. No chance of that happening as long as slavery prevailed of course, but ending slavery is the point.
Escaping and running en masse is a more realistic if less heroic plan (still pretty bold though) and my hat is off to Denmark Vessey. Too bad it didn't work.