Makes me think: as a loyal but devious Democrat, suppose the convention had indeed deadlocked with both Wilson and Clark stalling short of the votes required for nomination? Would the Dems have been desperate enough in the heat of Baltimore's Fifth Regiment Armory in the summer of 1912 to turn to an already-three-time loser in Bryan?
It's possible, but Bryan has to be daring. He must keep a very low profile and trust to luck that the deadlock will happen of its own accord. If he is seen as having
caused the deadlock for his own advantage, that will scupper him as it did OTL. Even if for some reason the Clark people aren't prepared to vote for Wilson, they will switch to Marshall or some other dark horse rather than let Bryan get away with it.
If they had, I suspect the result (say, a Bryan/Marshall ticket) would have been even worse for the Dems than 1908. I could see Dems outside the old South getting sufficiently disgusted that they'd probably just stay home and not vote. Could well be that TR becomes a third party president-although were that to happen, one has to wonder how he'd get any of his agenda through Congress having to rely on cooperation of the two major parties.
He wouldn't. A third party presidency would be a total fiasco.
In any case I can't see it happening. If the party has turned to Bryan of its own accord, without any evidence of chicanery on his part, there is no reason for its core voters to be particularly disgusted. And after all, even OTL the party
did do worse than 1908 - 41.8% for Wilson vis a vis 43.1% for Bryan on his last and poorest performance. But even the lower figure was enough to give Wilson a landslide in the Electoral College, and even Alton Parker's 37.6% would have done so. In 1912, the President was effectively going to be picked at the Democratic Convention, as in 1920 he would be chosen at the Republican one. In neither case did it greatly matter whom they nominated. He would have won virtually whoever he was.
Final point. Given Bryan's reputation (whether still deserved or not) as a dangerous radical, any defections from him will be largely conservative Democrats, who will mostly switch to Taft rather than TR. Even those (probably very modest) losses may well be offset by gains at the expense of Eugene Debs.