Sadly, it isn't. It's in the Stato della Cittą del Vaticano, SCV, an independent quasi-sovereign state. They even have a seat in the ONU. When I am in Saint Peter's basilica, I am "abroad". Mussolini did this awful mess in 1929 to rub himself purring on the priests, who rubbed themselves purring on him in return. Religio instrumentum regni, as ever.