Why bother about the Pope? His importance is very poor because his power is almost symbolic. In the civil war idea I'd like to think that the Pope is protected by right-wing parties, as you know the leftists don't care about the importance of the church.
Lot of people here in Italy are catholic, of course, but the Vatican don't have the resources to declare authority or independence.
In a plausible Twilight War, the Pope will stay in his Vatican and his presence will also be a guarantee to keep some kind of "moral order" and avoid the bombing of Rome. If Soviet or other countries will nuke Rome, what do you think of public opinion around the world? But, I accept that, if there'll be a nuclear escalation I don't know what can happen
