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By Baphomet, Horus, and the Moon Goddess, I stop posting and this gets derailed by politics?! I need to put this back on the rails.
OP, is there anything in particular you need? I've been dumping info on you, and I think you have enough for the moment.
When they find out, my understanding of PC logic suggests that at least one of them will try. If you use a NDE, that's the obvious way to get one. Start with innocuous instructions, and over time, bring them more in line with the conspiracy's goals and less with the party's. The character is going to be spinning a web of lies, and once he's thoroughly entangled, you can either keep tugging him towards the conspiracy's goals or have his mysterious patron confront him and reveal that he's part of the conspiracy.
I also like the Mason suggestion; along those lines, if you have a clueless Catholic layperson, see if you can get them going to confession and receiving spiritual guidance... which happens to be mostly temporal.
Chick doesn't explain at what level Catholics start participating in the conspiracy: the average layperson, whom he refers to frequently as "precious", is clearly deluded and not advancing the Pope's goals, but members of the KoC (who are mostly laity on the local level) are sworn to the pope's ends. Now I'm imagining them chasing your party with their silly hats and blunt swords, all drawn in Chick's style. It's pretty amusing. ( Which reminds me, I need to see if I could even join the Sovereign Military Order of Malta.) The average diocesan priest is probably an unwitting or self-deluded participant. Members of religious orders are obviously in on it, at various levels from the average brother, who obeys blindly, on up.