Someone might have mentioned this already, but, if at any point the Pope is incommunicado for any significant period of time, chances are good that another Pope would be set up somewhere else. With global communications thoroughly wrecked, I could see Popes springing up on every continent. This could lead to a Greater Schism.
In my Austrian sourcebook, I have an Austrian city-state set up their own Pope, claiming that the Pope in Italy is a communist puppet. It's more a play to gain support from Austrian Catholics than anything else. Any move to establish an alternative Pope would likely be an almost purely political decision.
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