Dent is that he's really not the White Knight that he's built up to be. Dent is a flawed character from the start. Among other things, he's a control freak. He is more than willing to cheat and deceive other people to get what he wants and to get his way.
This is all true, and if Harvey Dent had become an out of control vigilante after being horrible scarred... I would have bought that. We get a hint of that earlier in the film - he's willing to go too far in the name of what he wants.
But after the love of his life has been killed by this sick bastard the Joker, he's going to embrace existential uncertainy and kill in the name of that
... thus leaving the Joker unharmed but Comissioner Gordon not so.
See this is not something I buy. There's hints that Dent could go off into the dark end and become a guy pretty much out to get what he wants, but there isn't a logical sequence where this random chance is what he wants - I can't see any plausible scene between him and the Joker that doesn't end up with him trying to kill the Joker.
He may even realise as much as you postulate... but that would still require him to kill the Joker in rage and revenge and shame.
Sort of don't see a way this Dent can avoid this, coin toss or no. We needed more development here - a better look at his instability - then the film's running time or plotting could realistically allow.