A reply that wasn't going to happen.
if that's what your looking for, then you're better of going on your artistic fiat. There is the knowledge about the organization and there are secrets with in it. What is on the surface could be very different with what is in the inner workings.
In my experience, as what is defining Catholicism in view of current events, it is that it has many inner conflicts: the role of science in religion, secularism, internal and external politics, changing values of the world. The role of "magic" would change its face entirely and throw all this out of the window.
If you are able to follow current events, the chruch at present is slowly coming to a head with changing values of the world.
Another thing that may get in the way of magic wielding priests is the long history of Inquisition. They were one of the first to magic was condemn magic as hersey since the earliest days of the church and not from supernatural aspects. The Inquisition was one of the defining traits of relationship of the church and anything supernatural. That is why the church invites skeptics and has a love-hate relationship with secular thinkers.
If this inner conflict is too much, you can just make it all up and ignore the consequences of how it can change things.
If you consider to keep this conflict then you have to understand some fundamentals of the church's power. Understanding this, will give you a very interesting insight and material for intrigue and shades of gray game.
In this route the church doesnt have its own magic and mysteries instead it uses that of other religions and breakaway factions. You can make it that they may have acquired their magic from all the other religions and theologies they suppressed and destroyed (there are a lot btw, more than any other religion).
If dive further into it, you begin to find out where this power is going to preserve itself and build up an interesting web of intrigue for players to explore.
The role of the Catholic Church in Rwanda Genocide and Hitler's regime.