If memory serves me correctly, the decision to send the extra troops was tied in with the decision to re-look at the Iraq Joint Campaign Plan and the decision to send Gen Petreaus. While the "surge" is usually assocated with extra troops, it also featured additional State Department resources (ePRTs and an embassy crew that was was pretty much the DoS "A-Team" headed by Amb Crocker).
While this isn't any official view, I believe that the surge, in all its parts, played a decisive role in the Anbar Awakening because it sent the signal that we (the coalition) were going to be around for awhile. This gave the tribal leadership the confidence that they could deal with us and not be left out to dry. Prior to the surge, the key strategy was to turn the war over to the Iraqis as fast as possible. That is still a part, but the new strategy emphasized securing key portions of the population first.