I could see a peri-modern "crusade" into Italy, but I suspect the Ottomans would hold sway in Italy for at least a century due to the inevitable political conflicts outside Italy that would result from an Ottoman conquest of the peninsula. A century of Ottoman rule in Italy would probably not alter individual Italians' adherence to Christianity, but might permanently weaken Rome as the papal seat and center of western Christianity.
I think they could hold out for a century *at most*, at least in Northern Italy. While there was a lot of political fragmentation in the West, it wasn't all quiet in the East. One must remember that such an endeavor as conquering Italy would strip troops away from other frontiers, which the Ottomans' enemies would no doubt be interested in. Conversely, once they are landed in Italy, there's a very real possibility that the bulk of the army would be removed to deal with said threats/invasions/uprisings etc, leaving just an occupation force.
This ties into the more general problems of geography. One of the reasons the Ottomans did so well in the Balkans is that they spent over two centuries building a power base there, and therefore could easily project force into the surrounding areas. Italy is a whole other kettle of fish-there will be unfamilar territory, lengthy supply lines, including a sea crossing, and a disgruntled populace. Sure, some will collaborate, but I can't imagine the entire population of Italy automatically overcoming centuries of anti-Islamic indoctrination overnight.
Furthermore, the territory is not friendly to invading or occupying forces-lots of mountains, valleys, and narrow passages. Good ambush country, and it has a tradition of banditry. I can see this causing enormous problems for occupying troops.
Finally, I highly doubt that the other European powers would relenquish Italy that easily. While I can see them being otherwise occupied during the invasion, in the long term someone is going to feel threatened by it, especially if they get close to the Alpine passes. Even if none of the Heads of State act, there's always the possibility of a popular Crusade. While it may not be successful, it could at least fatally weaken Ottoman power in Italy, especially considering the other factors involved. Sooner or later, one of the other states, or an alliance, will take advantage of that and drive them South.
Of course, most of this mainly holds for Northern and Central Italy. Souther Italy is a different story-I can see the Ottomans holding on to it for quite a bit longer, or at least reducing the Kingdom of Naples to vassalege.
