Well, since Vandy, Mizzou, Arkansas and Georgia are already out, and two additional teams will be eliminated tonight, I can provide my personal guarantee that South Carolina will not be the first team out, despite the vitriolic and self-loathing commentary of some.
OP, if Carolina makes it to the tourney championship game with the two wins in your scenario, they would have approximately a 51% chance of getting in, per some recent reporting. Basically a coin toss.
Have to get past Auburn tomorrow, and if that happens, it will be the winner of Florida and LSU. Tough sledding for sure.