Okay I haven't fully articulated my anti-Jashin arguments yet, so I'm going to give it an attempt just in case you guys haven't considered these points before. Somehow.
I am fairly strongly convinced that the QMs don't have some secret Jashin +x to rolls modifier Akatsuki will be using in the battle. Similarly, I don't think Jashin will allow the likes of Itachi or Sasori any rerolls the way our FP does. I am 100%, absolutely convinced that Jashin, the in-game entity, can't affect our real life (or digital) die rolls, I am not nearly superstitious enough for that.
What I do think Jashin can do is act as a tag for Hidan. Hidan can personally receive some buff or mechanical advantage from his god. This is, after all, what makes him immortal, and may affect him in other ways.
I do not think Hazo's silent prayers will affect that tag in any way. I do not think Hazo will himself gain a similar tag, or achieve sudden immortality.
In short, I am very strongly convinced that this will do nothing for us in terms of actual, fleshed out, currently existing game mechanics.