For this particular issue, Apple allows apps to dynamically download Javascript and other web tech (in order for web browsers to work), and they explicitly mention that they're not into you pushing big updates:
provided that such scripts and code do not change the primary purpose of
the Application by providing features or functionality that are inconsistent
with the intended and advertised purpose of the Application as submitted
to the App Store.
As always, the App Review Team gets the final say on a case-by-case basis for whether you'll get through or not.IMO, Apple specifically carved out the exception for JS for WebKit/WebViews, to make using web views in apps possible. I'm quite certain they didn't have in mind React Native[1] auto-downloading JS bundles to bypass App Review. Apple wouldn't be a fan of that.
Now, the complete opposite of this is their favoured tech for developing new Apple TV apps, TVML, explicitly allows and is designed for updates bypassing App Review. In fact, most of the app logic and UI is delivered from your own server.
[1] Actually, the guidelines mentions 'WebKit framework'. Does React Native use 'WebKit framework'? Edit: It uses JavaScriptCore which I guess is a part of WebKit http://trac.webkit.org/wiki/JavaScriptCore