It's the reasoning for why South Carolina tried it that would be important. South Carolina would be attempting to secede after, more or less, a decision on a single bill that wasn't actually going to utterly shatter the existing economic structure went against them. That so lowers the acceptable boundaries as to when you could theoretically work for nullification or secession that it renders the entire concept ludicrous; the other southern states would turn on them so as to keep these sort of extreme measures available for situations that might actually require them.
Using military might to enforce compliance with federal law by a State which has not left the Union is one thing...that's what Jackson's Force Bill was intended to achieve and what many in the South supported at the time. Once the precedent is set that the Federal Government can legally use armed force to coerce a State, or make war upon a State, which has declared it's intention to leave the Union, however, the whole right of secession is invalidated. It doesn't matter what the reason for the secession was. The Pandora's Box is opened. And if faced with that reality, it is doubtful that they would have stood by and allowed South Carolina to be invaded and forced back into the Union. They would have been fools to do so.
The idea that the North could use this as an excuse, were South Carolina's nullification or secession attempts to be accepted, would be a major incentive for the rest of the South to distance themselves from Charleston.
The North might use South Carolina's secession as an excuse for secession themselves over the slavery issue, but they couldn't use it to justify Nullification, since Nullification would be a discredited doctrine.
The difference between what happened in OTL with Nullification and what would have happened in the propose ATL is that in OTL, Nullification was never discredited. A compromise solution was reached, and South Carolina never actually went through with it's threat to nullify the federal law. So Northern States felt justified in passing the Personal Liberty Laws which nullified the Fugitive Slave Acts. In the ATL, Nullification was tried, and failed, and thus would have been discredited as a doctrine.