I shall answer myself, since in wondering and writing about it, I think I know the answer.
Probably not. The issue is that a Dragon capsule (Cargo version) only has Draco thrusters for maneuvering. These have a thrust of 90 lbs. That is just too little to make much of a difference. Now if they could thrust for hours, sure that would help, but of course there is a fairly limited supply of fuel for each Draco on the Dragon so it is very unlikely.
Now Dragon V2 is a slightly different vehicle and will have 8 Super Draco engines, with a thrust closer to 16,400 lbs. That starts to be enough thrust to be useful, but again it is fuel constrained, since they are intended to be used for powered landing, and depleting that fuel supply before landing seems like a generically bad plan.
But even more so, the Dragon and Dragon V2 will have a trunk section attached that has the solar panels. (V1 has extendable panels, V2 looks to have them flat on the surface of the trunk itself, an interesting concept, which begs the question of why the change!)
The Draco engines can fire around the trunk, after all that is how it maneuvers in orbit and for docking/berthing. But the Super Dracos are meant to thrust after the trunk is discarded. So the trunk is likely 'in the way'.
It is interesting that while Dragon can fulfill upmass and downmass requirements, there is still a hole in the US capacity to reboost the station. (Which begs the question, could Dream Chaser or CST-100 reboost the station. Dream Chaser, no, since it docks tail end first to the station, which is where its engines are. CST-100? A good question).
Update 2024: And throw that one in the dumpster... They tested a Cargo Dragon reboosting ISS. Good news.
However, as predicted it did not have a great deal of effect. In a 12.5 min burn, it raised the altitude by 7/100's of a mile at apogee, and 7/10's of a mile at perigee.
NASA and SpaceX monitored operations as the company’s Dragon spacecraft performed its first demonstration of reboost capabilities for the International Space Station at 12:50 p.m. EST on Friday. The spacecraft’s Draco thrusters adjusted the station’s orbit through a reboost of altitude by 7/100 of a mile at apogee and 7/10 of a mile at perigee, lasting approximately 12 minutes and 30 seconds.
Next interesting question is how much fuel do the Draco thrusters have available for reboost, that is not needed for re-entry.
Of course SpaceX has already won the contract to deorbit the ISS in 2028 or 2030 or whenever they decide with a beefed up Dragon, using a bigger trunk full of fuel/thrusters.