While I do not know the internals, I believe the following statement is a good hypothesis;
Even when you have installed the application in release mode (in other words, there is no npm server and the app uses local .jsbundle) React Native has to keep two things working;
- A native thread to respond to whatever our JS code required (draw this, get geolocation etc.)
- A Javascript VM to interpret our code. (.jsbundle file included with the APK)
I believe, due to this added load, a react native app should consume more power, assuming everything else is equal.