Let us go back as far as 70 A.D. when the Roman army under General Titus invaded the City of Jerusalem. The objective has not changed much from then to the present. The objective was to take control of the temple. One can ask what does the Illuminati have to do with it?
The Romans realized it was not going to be easy to take control of the world so they devised a plan, the most clever deception introduced to mankind.
The temple of Janus, statue of Jupiter and statue of Venus were given a facelift so to speak along with new names.
The statue of Jupiter was re-named St. Peter, and the statue of Venus was re-named The Virgin Mary.
The birth of the Catholic Church!
When Loyola organized the The Society of Jesus in 1541 the intent was always the same, power!
In 1545 the Council of Trent was put together as a counter-reformation to the protestant movement.
Since then many counter-reformations were organized with the intent to infiltrate the protestant churches, to the present Council of Churches.
The Illuminati, Freemasons, The CFR, The Trilateral Commission, The Knights of Malta, many numerous branches are all traced back to the present day Vatican, the present day Roman Catholic Church!
Once again the intent has not changed one bit, Power!!!
The Roman Catholic Church has become more sophisticated behind the mask of religion and tradition.
So to answer the question....
It would be a very bad day for the Vatican if their records were opened to the public.