You don't have to win SC. It's definitely not part of Pataki's path to victory.
But you have to be on the ballot there to be viewed as a legitimate candidate. Otherwise you'll fade into irrelevancy after New Hampshire as the media pretends you don't exist for the next few weeks.
And Pataki has no path to victory.
But let's say Pataki surges (yes, I know, I have him at a 0% chance of winning the nomination, but still) and gets 3rd in New Hampshire, and elects to stick it out to Super Tuesday. He still wouldn't be a force in South Carolina. I see little real difference between placing sixth or seventh in the state and not being on the ballot. The media attention in the days leading up to a given primary is typically limited to those candidates who are most likely to win the primary or need a "good enough" performance to continue.