No, it wasn't. The Catholic Church had separate-from-the-state but binding authority in some areas of life, and something like extraterritoriality in much of the Western world, but it wasn't the government ever over any but a few relatively small parts of the Western World (well, technically, never over any of it, though certain clerical positions were conjoined to positions of state authority, either lower in the feudal heirarchy or, occasionally, actual sovereignties like the papal states or one of the co-princes of Andorra.)