This is factually incorrect. The Stato della Città del Vaticano has a seat at the United Nations.
The Catholic Church per se, has existed since Pentecost. Vatican City as presently constituted as a City-State was established by the Lateran Treaty in 1929.
When Vatican City ceases to exist (I suppose when the Muslim Cultural Enrichers lob a nuke at it, probably called "Abd Allah" or "Shaitan") the Catholic Church will still exist. And through eternity.
Who run Bartertown? Master Blaster.
Who run Vatican City?