The Vatican as a nation-state? As a matter of protocol, sure. No standing army unless you count a company or two of Swiss Guards, no political agenda, no influence outside it's 110 acres except regarding morality. And if people should reject statements on morality no repercussions except that they get prayed for. Just like Caesar's empire.
I would say that you cannot have an organized religion without some type of structure, not particularly what we might call a government. (See Islam for that.)
