For the most part, no. Secession was almost always premised on the notion that either states would go out in a coordinated fashion and then unite together or they would reach some prior arrangement and secede as a bloc. From around the late 1840s/early 1850s onward, South Carolina politics largely ran from the more radical Separate State Secessionists to the moderate Cooperative State Secessionists. There are Unionists still around, but they're politically marginalized.

The Cooperate State Secessionists had a good case on the facts, but less so on the history. If South Carolina bolted on its own, like it threatened in the Nullification Crisis, then the South might just leave it out there to wither on the vine. The reputation that the state had gotten (and deserved) for wild-eyed radicalism worked badly against it here. Back in the early 1850s, the vision was for some kind of all-South convention which would issue ultimatums. Then the national government would capitulate or the whole section would leave as a unit. A convention for that end happened at Nashville, but there were enough moderates involved that nothing came of it. A rump body dominated by radicals rejected the Compromise of 1850, but that was about it.

The disunion action then shifted to a conspiracy between, mostly, the governors of South Carolina and Mississippi. The idea was that if two states went out in a coordinated way, it would start a bandwagon effect. That went double if Mississippi was one of them because it didn't have SC's problematic reputation and the state's political style was much more popular than SC's. In a coordinated move, you would have the old South and the new South together. But they could never get the timing right and the effort fell apart for delay.

From this, South Carolina radicals learned that you had to do counter-revolution in a hurry. When the moment came, they dared on their own...but not really. Formally, SC seceded to be its own nation. The bandwagon did kick in. There was no delaying and risking some new compromise to get moderates back into the national fold. Unlike some other secession proceedings, they didn't explicitly look toward a slaveholding union.

South Carolina's act of secession is unilateral in one and a half senses. It's unilateral in that the National Government was not asked to concur, which is usually the most important sense. But it's unilateral, kind of, in that it's not done in formal concert with another states' secession. Informally, the picture is more mixed. Cooperationists in Columbia still wanted proof that the promised bandwagon would come before agreeing to anything and the fact that only SC had kept its legislature in session through the election meant that official action elsewhere would take a worrying amount of time. To answer that, the Separate State crowd had only letters from other states. Nor did those letters indicate an unambiguous determination to bolt. There's an element of you-first-no-you-first in this. SC wants proof others will follow and others want SC to go ahead to stiffen the spines of waverers at home. To give you an idea, here's some of what comes in from Georgia:

"Do not understand me to say that I am entirely without fear of our state," James Mercer Green wrote Gourdin from Macon. But "we all think here" that "the stern march of events will drag us out, if the cowards do not go willingly." So too, John M. Richardson of Perry, Georgia, warned Gourdin that cowards here "fear the possible consequences of secession." They forgot the "certainty" that Linclln's rule "must lead first to the formation of a black republican party in our midst and then to a civil and servile war." Thus your [SC's] "delay ... will injure us." But speedy "action will exert a great influence.

This was a serious problem for the Separate State movement and they had to deal with an opposing proposition to delegate power to call a secession convention to the governor, if and when he had assurances that someone else would to too. A majority preferred immediate action, but the SC constitution required a 2/3 majority to call a convention and the cooperationists had enough votes to make that rough. For that matter, the bare minimum on a vote like this did not exactly telegraph strength and resolution. There was a strong sense that secession should have unanimity, or at least close to it. Disagreement in SC, cockpit of counterrevolution, would not set at all the right example for other states.

The immediate fallout from the clash is a compromise timetable that puts the secession convention on January 15, with elections for it on the 8th. That passes the SC senate 44-1. This was all decided in early November, so that's a long time to kick the can down the road. The radical plan was to hold the convention on December 17. By that time, someone else might have gone first.

Part of the problem for the radicals comes down to their reliance on previously secret correspondence and part of it from their own reputation. Actual fraud isn't suggested by contemporaries, but it would be easy enough for the radicals to only show letters helpful to them. Being secret didn't help. Nor did the inability to see the men writing them and judge their sincerity in person.

A coincidence intervenes on the radicals' behalf. A big rally had been set up for Institute Hall in Charleston. It happened the night of the Senate's decision for a delayed timetable and coincided with the completion of the Charleston and Savannah Railroad, which was finished two weeks before. The initial celebrations took place in Savannah, where the Georgian hosts gave assurances to anxious Charleston merchants that Georgia was with them. That all took place on November 2, before the election. More or less on the spot, the Charleston crowd asked the Savannah types to let them repay the favor with a big party at the railroad's other end a week after. that was November 3. The Savannah crowd agrees and they set the date for November 9. That's the same day as the SC Senate voted.

The Georgians arrive at three in the afternoon, after the Senate vote. They get the grand tour, have a big feast and the usual amount of alcohol. Lots of mutual toasting ensues. The Institute Hall rally is running at the same time. A Charleston merchant with Savannah connections picked out some of the most likely Georgians and ushered them over to talk to a crowd of north of a thousand Charlestonians. The speakers include Francis Bartow, an old time nationalist who had urged South Carolina to caution, but now agreed that if they went, Georgia must go with them.

It's an assurance, in person, not just of sympathy but coordination. Furthermore, it came from an avowed Unionist, an ex-Whig even, who urged action at once. The radicals could not ask for a more ideal spokesman. Other speakers followed in similar vein at Institute Hall and at the big party from which they'd come. Caught up in the moment of it, the mass meeting telegraphs Charleston for immediate secession, then arranges a special train so they can go up the next day and repeat their demand in person.

Here's the effect they had on one guy:

Henry Ravenel, formerly a Charleston delayer, explained in his diary why reasonable expetation had now turned his head. "I have heretofore always opposed separate state action, he firrmed, because "we could do nothing successfully alone-but in join action we can accomplish our deliverance." Now, "I believe we have assurances" of "co-operation. ... That contingency now seems so sure, that I approve most heartily [of] the intention of our State to secede first."

None of these men are capable of actually speaking for Georgia. They're pre-selected just like the authors of the letters made public were. But having them around in person is enough to reinforce the questionable impressions given in writing. They become more credible still when news hits Charleston that Robert Toombs, Georgia's senator, had resigned. There had already been considerable resignations among SC's local federal officials which were understood as preparatory to secession. It was only a rumor (and Toombs hadn't resigned yet) but it makes the three Georgia speakers look like the start of an avalanche. And if everyone is going out...then what's it say about those committed cooperationists who still want delay? Maybe they're abolitionists. Traitors. When that kind of paranoia hit the South, experienced politicians knew to get out of the way and prove their bona fides.

That brings us to 4:30 PM on November 10, just about twenty-four hours after the Senate went 44-1 in favor of the delayed timetable, the House went 117-0 for the December 17 plan. The matter went back to the Senate, which concurred 42-0. The elections took place in early December, the convention met on the 17th, and South Carolina dared.

All of this, and some more complexities I've passed over, makes it hard to decide who really prevailed in South Carolina. The separate state bloc got their individual action, but they got it because South Carolina received critical, if informal, assurances from Georgia. Everyone following South Carolina out does so with the knowledge that it's gone and that they share a common interest and convenient geography. Things quickly turn into a stampede:

SC: December 20 MS: January 9 Florida: January 10 Alabama: January 11 Georgia: January 19 Louisiana: January 21 Texas: February 1

The other states might have gone out anyway, but the way things happened they had South Carolina's example to follow.

Sources

My narrative here is William W. Freehling's version in Road to Disunion, volume two, as are the quotations. He also addresses the 1850-1 secession conspiracy in volume one, as does David Potter in The Impending Crisis