Don't kid yourself Hagel, no one would've voted for Harding with foresight. Any historian could tell you Cox was the better candidate.
I think it definitely would have been closer that IRL if knowledge of what was to come was available, but Wilson pissed off too many German and Irish Americans for Cox to prevail. Plus, electorates tend to be shortsighted, so saying your opponent will be unprecedented prosperity for nine years followed by a horrific depression probably would not be that persuasive.