That might be an oversimplification, but since it was the final result it's true enough.
As far as an implied secession option in the constitution. Since Southern states were forced to ratify the 14th and 15th amendments to be admitted back in the Union after the war, it certainly seems like they had effectively opted out previously.
they were never out of the union. They had to ratify the various amendments to regain self government after their insurrection.