First the control of the Organisation would have to become more localized in the minds of the Rank and File. This has already started to happen with the recent change in who comprises the Faithful and Deseret Slave ( used to be all the Anointed Class and is now more localized in the Governing Body). While the Watchtower Bible and Tract Society has ofically changed their teaching it will take a while before it filters down to the rank and file. I would imagine that the average Jehovah's Witness has a more nebulous understanding of who the FDS is and how they guide the Organisation(still imagining it to be all Anointed people). It will take time and more pushing of the 'new light' before more hope and trust gets put into the hands of a few men insted of some undefined nebulous group. If this happens then it might become commonplace for the rank and file to know the some of the GB members by name, as they would be rockstars of the faith. If this realized localization of power is well understand by all Witnesses then they are set for potential disaster.
A huge scandal would have to hit the GB. It could be a public scandle of any nature: a new group trying to claim power, catching GB sessions on film where they bash the rank and file, intentional abuse of finances, etc. The point is that the controlling power would have to be discredited to the point they could no longer be trusted by the rank and file. This is where it is so important for the JW's to have all trust vested in a few men. When they are discredited there is no where esle to turn for leadership, its not like they could say " oh well, the organization was always directed by the whole Anointed Class anyway...so all we need to do is replace the GB members with more people from the FDS. So, really the FDS is still and has always been guiding the Organisation it was just a few bad people within the FDS and not the FDS as a whole". That line of reasoning would not even be an option if they realise the FDS and GB are one in the same.
So, if the GB becomes publicly discredited there is no leadership in the minds of the rank and file. It would be like a nation without a king or Roman Catholicism without the pope. Then a fight for power would ensue that could lead to a total collapse of the Watchtower Society as we know it. I doubt that it would cease to exist all together, but I would hope that the new controlling power would be softer to the rank and file. Hopefully it would be less of a cult and not as damaging to members.