Will the Vatican's defense of "Those few pervert priests technically didn't work for the Vatican" succeed?

Yes, it will probably work. The Vatican cannot be sued because it is technically a country, and is diplomatically recognized by the State Department. You can't sue the pope in the US for the same reason that you cannot sue George W. Bush or the State Department in Jordan for negligently prosecuting the Iraq war - they have a form of diplomatic and sovereign immunity. Those immunities can only be waived by treaty. This actually is the lead argument in the pending KY case - the media is focusing on the employment law defenses because they are easier for the public to understand. No case has yet succeeded in impleading the Vatican or the Roman church, as opposed to the local bishoprics and dioceses. If you think of the Vatican as a country instead of as a corporation, then the decisional law makes more sense.