I about fell off my exercise bike when the PBS movie: “In Search of Shakespeare” suggested as much.
I should clarify that the movie conclude one way or another but suggested it was possible. I had never heard this or the reasons why so it made quite an impression on me.
This was only talked about in passing but from the content I remember it was pretty likely that his father was in fact Catholic.
Another interesting thing from this DVD was a very brief appearance of Patrick Stewart aka Jean-Luc Picard as Hamlet.
http://www.shoppbs.org/sm-pbs-in-search-of-shakespeare-dvd—pi-1452173.html
“I should clarify that the movie conclude one way or another but suggested it was possible.” should be:
“I should clarify that the movie DID NOT conclude one way or another but suggested it was possible.”