It really would have been hard for Edwards to win the primaries, without a POD quite far back. Obama would probably have to decide not to run, or his campaign would have to fizzle early, and Hillary would have to be a weaker frontrunner from the beginning. If she were subjected to the 'electability' argument for nine months from Mark Warner or Evan Bayh, the 'conservative centrist' vote could be split, allowing Edwards to take the high ground amongst liberals and blue-collar workers.
So Edwards wins Iowa, survives New Hampshire, goes all-out in Nevada (his criminally weak performance there this year was because the media oxygen had been sucked up by the Hillary-Obama duel, and through very poor organising), wins South Carolina, and does well enough on Super Tuesday to be the presumptive nominee. It's possible but not likely.
So then Hurricane Hunter hits the Edwards campaign. Presuming it hits at a similar time of the year then I think there's room to try and tough it out: after all, there's simply no other pick, in the absence of a veep. Bill Clinton survived Gennifer Flowers, Richard Nixon survived the slush fund, Grover Cleveland survived an actual love child: there's precedent for Edwards going the whole bitter slog to November.
Of course, it's entirely possible that defeated rivals could revive their campaigns, trying to poach his disillusioned delegates, and we have the mother of all battles at the convention. Or that he could simply drop out and endorse another candidate, who would have about as much chance of winning the eventual election as I do.