Sullivan was quite spent by this stage, but it was also arguably his greatest technical performance. He didn’t rush in trying to take Kilrain’s head off like most Sullivan matches, he broke him down over a period of time and didn’t try finishing him until Kilrain was a literal walking corpse. According to Adam Pollack’s Sullivan book from 2016, Kilrain thought that it was not wise to rush Corbett and that Sullivan should’ve instead been “calm, consistent and methodical in his attack.” Assuming he takes the same approach against Corbett, instead of trying to rush, Sullivan should be able to win by the later stages of the fight. Corbett usually got finished eventually by the best punchers he fought and a closer to prime Sullivan was arguably the best puncher he ever fought.
So by this stage Sullivan is a shadow of what he was in 1882, but still has enough left in the tank to beat Killrain. I guess it would depend on the rules.