Doubtful. It is not conclusive, but according to this:
the fifth card had been discarded, and its replacement had possibly
not been dealt.
I'm not sure what house rules were in place at the time, but it seems likely that after Hickock was shot, the game - or at the very least the current hand - was abandoned. With the hand abandoned and a man just shot, one would only have the words of the players themselves as to what they held. Even if there were records to this effect, the reliability of such records would be in question. Even the actual hand of the man in question, of interest because he was the deceased and thus was unable to protect his hand, is not entirely known - the actual identity of the fifth card, as well as whether or not it was the original or redrawn card is not known for certain.
Even ignoring that problem, if the replacement had not even been dealt, then nobody would have "followed the rabbit" to see who would have won, and even if Hickock had been dealer (which seems unlikely), there would have been additional draws and betting behind. Is it even recorded how many other players were at the table at the time and how many were still in the hand? Even if we had a complete account of what every player held, it is very unlikely that the final outcome could be determined, even assuming every played stayed in until showdown.
What we do know is that Hickock was not shot by anybody currently in the hand - the man who shot him had played the previous day and approached the table from the door and shot Hickock in the back. So from this we can conclude the actual shooting had nothing to do with the cards in the current hand, but beyond this there isn't much we can really say.