The very short answer? No, not a shot in hell.

Smith didn’t have any of the party apparatus that was necessary in the era to win major office. His Reform Party really only had organization in Illinois and a few other states. Of course he was assassinated before ballots were made up, but given where his party existed and where the campaigning was happening, it’s not likely that he’d have been on the ballot in more than a dozen or so states. And the meeting minutes from the Council of 50 meetings suggest that everyone involved in the process understood that. I think his first choice for VP candidate James Bennett summed up the thoughts on success rather well:

“if you can by any Supernatural means Elect Brother Joseph President of these States, I have not a doubt that he would govern the people and administer the laws in good faith, and with righteous intentions, but I can see no Natural means by which he has the slightest chance of receiving the votes of even a one state.”

It’s hard to tell, for certain though, how serious the bid was. The men involved in the campaigning would generally admit to the difficulty of successfully electing Smith. But would rarely admit that they thought it might be impossible. To the degree they would admit that, it was usually followed with a, “but with God all things are possible.”

It should be noted that throughout the campaign Smith and his campaigners never stopped any of their alternate plans of finding a new place to live. It was during his campaign that Smith tried to get a commission as a general with the purpose of wresting the whole of Oregon from the British; petitioned Congress for a territory in the interior to be established for Mormons; talked to the British about buying Vancouver Island; asked Sam Houston about buying part of independent Texas; and more. So the whole period was very much an attempt to secure the long term safety of the Mormons by whatever means panned out.

The presidential campaign was very much a Hail Mary and as much an attempt to gain publicity and to try their cause in the press as it was to actually gain the office. At worse they expected to gain sympathy among the common Americans… but with a tiny bit of “I have a year now that I didn't have before. And a lot of things can happen in a year. The king might die. The horse might die. I might die. And, who knows? Maybe the horse will sing.”