react native - should I run the server with the command react-native start so that users can use the app?

Hope this question understand when you react-native start What are the difference between these React Native start commands? React-native start should use in development environment. When your device or simulator connected to server

I think you mean building the apk file by "deploy". If i'm right and you have used some APIs in your app, you should run the server of your backend app to let your react native application send and receive data.