Some Democratic elites fear that the answer is yes. For example, the head of the DNC, Howard Dean, has expressed such a concern:
bq. The idea that we can afford to have a big fight at the convention and then win the race in the next eight weeks, I think, is not a good scenario.
Does a divisive primary hurt the general election chances of the nominee who emerges from that primary? In short, the answer is no. Perhaps the most relevant study is by Lonna Rae Atkeson (here, gated). She examines presidential elections from 1936-1996 and finds that the relative divisiveness of the two parties’ primaries is not related to the general election outcome, once other factors, namely the state of the economy and the popularity of the incumbent president, are taken into account. The logic is this: a divisive primary is more likely to arise if an incumbent is unpopular or presiding over a weak economy, simply because this incumbent will attract more challengers. Leaving the economy and presidential popularity out of the equation risks overestimating the effects of divisiveness.
This November’s outcome will depend more on fundamental conditions in the country, especially the economy, than on the tenor of the race between Senators Obama and Clinton.
[Addendum: See also more (and better) discussion of the issue by Josh Putnam over at Frontloading HQ.]