I am not an expert in Tor, although, like many open-source programs, Tor is written in C and I can read C. What Tor (and Tails) will do for you is to anonymize your IP address to a very high probability. In other words, if you visit CathInfo via Tor, Matthew cannot tell what your true IP address is, only that you are coming from a Tor exit node. Now, if he wants, he can block all of the Tor exit nodes (they're public), but if he does, he'll risk blocking someone in Saudi Arabia, Iran, or some teenager in some wacko Protestant fundamentalist home here in the US whose nutty parents are spying on him/her to see if they are visiting some of the "Cathlick" websites. If "junior" is reading this post and decides to use Tails, then Mom & Dad (and, for that matter, the US government) will have no idea that Junior is learning all about the One True Faith or that he/she is posting messages to "Cathlicks" like us.
On the other hand, if you use Tor to make a bomb threat to your school and include your name, address, and phone number, then, no, Tor will not provide you with any anonymity whatsoever. When the FBI and police show-up, you could, of course, claim ignorance.