I'm a bit dissapointed that you can't 1527 the Pope ingame, due to limitations. Sad
The mod designers did miss a trick or two - for example, the Avignon Papacy in the 14th C. - but having that while also having a Pope who could survive the sack of Rome and still be contactable is probably too much of an ask. It's true that Rome falling into foregn hands does not hinder The Pope's ability to call Crusades. It
may hinder the giving of gifts of buildings and such, depending whether that is built on unique code or simply uses the standard AI gift mechanic between civs. However, the simple WB cheat I detailed above allows you to sack Rome and play on without a Pope. You just can't sack Rome and have the Pope survive. *
The simplest way to allow the player to legally "1527" the Pope in-game would probably be to make Rome unrazable and set The Pope to respawn a few turns after Rome is captured. A mechanic for this already exists in the game - the same unrest machanism that makes controlling Jerusalem a headache could be used for Papal loyalists revolting, with a high probability of the revolt succeeding. If the revolt succeeds, The Pope would respawn in Rome, and his city would be restocked with a good complement of up-to-date defenders.
However TTBOMK, development of RFCE is effectively dead, so don't expect to see that anytime soon.
* ETA: It occurs to me that hiding an unreachable 1-pop Papal city on the map might create a Papal civ that can survive the sack of Rome. You then simply flip Rome back to him a turn or two later, the implication being that you can capture Rome, but you can't keep it. There's already the little Rhye's Catapult enclosure in the Sahara, for example (the Catapult appears at 32,0); you could add a second enclosure nearby for the Papal bolthole. Or carve it out of the top right corner of Russia. Of course, the AI would probably spend the whole game trying to connect the two cities by road ...