And if so then what would that mean? It would just be changing the definition of a word, semantics.
It would mean that we can stop using "it's supernatural" as an excuse to exclude a topic from inquiry. Folks do that. A lot.
Would it somehow change the reality itself? No. I guess if you choose to define nature that way, then you could view God as existing naturally. However I don't see why that matters once again. Does that somehow mean God doesn't exist or that he didn't create the universe? Does it somehow mean that heaven wouldn't exist or that we humans didn't have souls?
It means that none of those things are in-principle beyond the scope of the scientific method to detect and determine. It means that we can't just make stuff up and claim it's both real and "outside the natural universe" or some such nonsense just to dodge questions, as is common from religionists.
I could define "natural" as something that 'exists' and then say "Therefore God is naturally occurring." but what does that change other than our own interpretation of the same exact event?