Short answer: Some will, but probably not enough to matter.
The antics at the convention, especially on the first day, have gotten some Democrats worried. Bernie himself is not at fault for this — since the end of his campaign he’s striven mightily to re-unify the party, even getting booed for it on Monday by some of his own supporters (which raises the question of whether they can still be called “Bernie supporters” at all). Yet the eruptions in Philadelphia continue. The Russian e-mail dump has fueled the anger, as Putin obviously intended it to do.
However, the crucial words in the paragraph above are “at the convention”.