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.
What it will do, however, is affect Hazo's own characterization. He will, forevermore, be the guy who silently prayed to Jashin during the most important moments of his life. He can't 'haha I was just kidding guys, Hidan was threatening me!' his way out of this genuine personal belief. I do not think the very slim odds that the QMs will see that line and decide to write up a whole new mechanic just for this fight is worth the hit to characterization that will mar Hazo forevermore.
Moreover, what it could do that is even worse, is actually empower Jashin. Especially if the QMs DO go through the trouble to write up a whole new Jashin luck mechanic. At that point, Jashin will be absolutely cemented as the next big problem, the next arc of the story. What will we do after claiming the rift and bringing back the dead? What will we do when the likes of Jiraiya and Naruto can handle world politics and there's no more major antagonists? Can we win the game, bring uplift to the masses? NO! Because the next antagonist will be a fucking evil god that we willingly empowered, and we'll have to deal with that flavor of bullshit next. Dragons -> Akatsuki -> Out Entities. It's the natural escalation, really. How many Japanese stories go from fighting rats or whatever to trying to kill god with the power of friendship? Hell, 'Naruto' is one of those stories too.
Hard pass, for me. The chances that Jashin will be a problem down the line is much, much higher than the chances that he'll somehow be helpful during this fight.