Has a 3rd place 1st round candidate- ever ended winning?
Ever ended up winning DNC chair? Probably not. Though something similar ended up happening in Canada in the Liberal Party's leadership race back in 2006, when Stephane Dion came from third (and nearly fourth) in the first round to win the leadership, so it wouldn't be totally unheard of for a third-place finisher in the first round of a major party's leadership election to end up winning.
It did not end well for him or the Liberals.
https://en.wikipedia.org/wiki/Liberal_Party_of_Canada_leadership_election,_2006#Convention_results