It wouldn't work, since the pope has a really small realm. You could just come in, and assault his holdings with your retinues, and the war would be over before the other rulers could gather their troops. Anyway, you can have the pope as a vassal only if you're emperor. I've seen aggressive papacies, but they're few.
Now, its not about subjugating the papacy, but you can bet that if some random duke in the middle ages declared war on the papacy for any reason, the entirety of catholic europe (or at least the biggest nations) would band together to wipe him off the face of the map.
Now, I would assume defense would work like a crusade in that it would draw tons of catholic countries in to defend it.
It would actually be pretty hard, assuming that you aren't empire sized that is. If all nearby italian countries rushed to their defense, and the pope instantly hired as many mercenaries as possible, by the time you could land any soldiers, they could easily get 30k troops defending faster then you could reasonably get any non-reutine troops there. In another month or two when the HRE+England+France got over there (which is probably ablout how long it would take you to gather all of your troops), there would easily be enough troops defening to fight off anything short of a empire size force.
Using just reutines would be tough, you would probably need +10k to take the entire province without regular troops (which if you could do, you would probably have a large enough empire to take thm in a regular fight), and even that could be countered by the pope just hiring a bunch of mercenaries and rushing you before you could win all the sieges.