I don't think so. There was a very informative article in National Review a few months ago right after he dropped out, and all indications are that his political career is over, or at least on hold. He decided not to run again for the U.S. Senate because he was almost certain to lose, and when you add up his delegate totals you realize that he got more media coverage for a guy with 15% of Democratic voters than anyone else would have gotten.
Plus, just look at the bunch of has beens in the Democrat party who aspire to high office. Not a whiff of charisma among them.
Actually if Edwards wants to maintain higher aspirations, dropping out of the Senate is not necessarily a bad idea. He could go the Carter route, spending the next few years building up and running a high-profile charity. Lots of positive pub opportunities, 'altruistic man of the people' image builder, without the negatives of 6 more years of on the record Senate votes, yet he still can claim that he already has national political experience(thus 'qualified'). Especially if Kerry loses and the GOP retains the Senate, there will be a major housecleaning(wait, this is the left, make that a purge) of the Dem party, which he gets to sit out fairly unscathed and then jump in front as an evolved 'new leader' for the Dems.