IMO, Roosevelt could win the election - and if so he'd be taking office early. Wilson had of course planned on appointing Hughes as SecState, then resigning along with VP Marshall. It's probable that he'd do the same with TR, who in this scenario would be taking office within weeks of his election. I expect that Roosevelt's Vice-President, who per the Constitution would actually be taking office later than Roosevelt on the scheduled March 4, 1917 inauguration, would be a Midwestern isolationist and a political moderate to balance the ticket. Perhaps Elmer Burkett of Nebraska, Fairbanks' only serious challenger for VP in 1916.
Roosevelt would ironically have handled the war little differently from Wilson if elected in 1916. The main differences would be in how Roosevelt handles the peace as I've mentioned previously:
All the same, had he been elected I actually don't think he'd behave much differently from Wilson as a wartime leader. He would build up defenses and seek to arm merchant vessels, before seizing upon the Zimmerman telegram and the return of USW as a causes belli. He would advocate for a League of Nations of some sort (I've read that he supported an international "League of Peace" with a standing force) but unlike Wilson he would still die early in 1919 and the new President goes to Versailles. Much like what happened with FDR and Truman, ironically.
So President Burkett goes to Versailles, then probably loses in 1920 to Ohio Governor James M. Cox. The 1920s will likely be a Democratic decade. But I wonder if FDR would remain a Democrat - as I've mentioned in earlier posts TR has good reason to keep him in his administration. By 1920 the younger Roosevelt may be under pressure to switch parties and run with Burkett as his Vice-President.