Yes, but it wasn't one of the first states to do so.That was fortunate, when Sherman arrived there after putting the boot into South Carolina, which was identified as the state that started the war.
Because Lincoln had virtually declared war by calling for volunteer-troops, and North Carolina reluctantly decided to join the other ten Confederate states. It was the last state to secede.
No, it wasn't. The cut off was the new state of West Virginia which was established because they wanted the Union enstead of the Confederacy. So North Carolina was not part of the Union.