Was Shakespeare a "secret Catholic?"

What did Shakespeare do during the "lost years?" Father Andrew Headon, the vice-rector of the Venerable English College in Rome believes the playwright spent the years in the Eternal City and was a "secret Catholic."

Father Headon believes he has documents that can prove the claim, including a leather parchment "signed by Arthurus Stratfordus Wigomniensis in 1585, Shfordus Cestriensis in 1587 and Gulielmus Clerkue Stratfordiensis in 1589."