Is this only for React Native and not web React?
While you can't just port over, the way you think about components and your API endpoints can be re-used. It's also nice that they both work with components which allows for less "context switching."
It is about whether the source application code can be the same. Today it isn't. But why not create a set of source compatible components that render to Android, iOS, and HTML?
I've seen projects approach this and I think it is a good idea. You get the typical lowest-common-denominator problem but if you have a decent way to mix in platform-specific elements where required, what is the downside?