I think he would, at least if he had come close to winning the nomination. His supporters would have a plausible argument: "See, Udall's defeat shows that only a southern moderate like Carter can win--we've lost three times in a row now with northern liberals."
After all, Carter lost the race for governor of Georgia in 1966, and that didn't prevent him from running (and winning) in 1970.
And the 1966 loss AFAIK apparently helped make him an evangelical back then.
How would Carter handle the inflation crisis? Would Ford have appointed Volcker or would Carter have done it?