I've never used React Native so I can't say anything definitive.
My understanding is that you can write JavaScript while using React Native, so some parts of the Esri JS API will probably work, similar to how you can get parts of the API to work in Node. Other parts may not work, as React Native does not target a browser and parts of the JS API rely on the browser API.
That last part is a problem when it comes to displaying a map and view. I don't see how React Native could translate the whole JS API view rendering process into something that would make sense to Android/iOS. So my guess is that this isn't really possible to use the JS API to render a view in react native.
You might have better luck with the ArcGIS Runtime SDKs for Android and iOS. Here's a repo that looks like it has a proof of concept: GitHub - glazou/react-native-arcgis-sdk-demo: Proof of concept - Use ArcGIS Runtime SDK for Android ...