I think PDR could probably do a very good job with the visible portion of the quarter. However, looking at how the bumper is now hanging against your quarter panel, I think you probably have more damage on the lower quarter than can be repaired by PDR. The rear portion of your quarter looks to be pushed in and it would likely need to be pulled out to get it to properly align with the bumper.
I would get with a good PDR tech to see what can be taken care with PDR and then look at conventional repair on the rest because the bumper may still not align properly after the PDR.
If you get the estimate from Geico (or any ins. co.) , don't cash the check until the all the work is done to your satisfaction if you decide to go that route. There's is probably more damage under the bumper that should be addressed than they will put on the estimate initially without taking the bumper off. Hope this helps.