Pretty much no way he could win because it was such a Republican year. Indeed, he'd have even more problem because unlike Cox, he'd be more tied to Wilson, who had kept us out of war but then gotten us into war and the nation wanted to retreat from anything to do with international affairs.
Cox may have been a running mate, though FDR is also possible.
This makes 1924 interesting. With Cox not having lost in '20, he might manage to win in '24, although nobody really had much support the first 5, 10, 20, 50...ballots.