I guess what you're asking can be split three-ways.
One: What would happen if a religion just *happens* to be correct? Like, by chance the universe works the way the religion says it does? That'd be... interesting, I suppose, depending on what the religion is. Could range from "Huh. Cool." to "Overturns human understanding as it stands" depending on a) how correct they got, and b) whether it's correct as in gets our universe correct as currently understood, big bang and all that, or if the universe instead turns out to not be how we think, but instead be how that religion conveys it. Flat plate on the back of four elephants and wot-not.
Two: A religion that attempts to change and correct to fit the facts as we know them. It'd be cool, and noble, but I'm not sure if it'd change anything major. Doesn't exactly fill a void or give new knowledge, it'd be mostly coat-tail riding.
Three: What if the world actually had supernatural entities and phenomenon? Well, after we started understanding them, to the extent we can, they'd cease being supernatural and just become a natural part/effect of the universe, at least the parts we can see/feel/experience/measure. Everything else, we wouldn't even know we didn't know them; we'd think we had the whole puzzle. For all we know, electrons are the intrusions in our world of fairies dancing in another universe, but because we can only see, measure, feel, experience, the electron-part of this weird fairy-dance, we have no way of knowing that electrons are actually supernatural. They'd just be a "natural part of the universe" for us. Same as anything else supernatural. The intrusions, measurable effect on our world would just be a (seemingly whole) facet of our naturalistic universe, working in ways we can't really grok because we're missing a piece of the puzzle, but because we'd have no way of knowing we're missing something, we'd just assume it's a quirky mess. If it even is, it could look whole. The only way we'd know we're missing something big/supernatural, would be if an actual intelligent being were to communicate and say "Yo. You're missing something." and even then, depending on how they communicate, we could still miss it.