|Will he? Won't he? Should he?|
I suspect he would position himself ideologically between Clinton and Sanders, offering a more liberal yet still 'mainstream' option. He would pull votes from Ms. Clinton - probably less so from Sanders, whose political base is the left wing of the party. Since it's hard to imagine someone running from Sanders' left, he'll keep the support he has - he's just unlikely to be able to expand it. Certainly Biden would benefit from those Americans who are uncomfortable with a woman in the Oval Office - we are, among other things, a fairly misogynist nation, and Biden would be the choice for Democrats who fall into that category.
He'd essentially be offering an extension to the Obama administration, just as Bush the Elder offered another term for the Reagan White House. Those who understand how much Obama remarkably got done in the face of the worst obstruction in decades would find that desirable, while those who are uncomfortable Obama's foreign policy, his support for the intelligence community, his war on whistle-blowers and his relentless pursuit of bipartisan solutions might be less pleased with the thought.
At the end of the day, I suspect he'll decide not to run. He can't win, and he'll only weaken the Clinton brand - she'll still be the nominee, but she'll arrive at the position after a more divisive, expensive primary season. If he does end up running, however, it leaves open an intriguing question - who would Barak Obama end up endorsing?