WordPress REST API has nothing directly to do with the theme, REST API is in the WordPress core, and any plugin and theme can be made to support it. Normal WordPress themes don’t use REST API: it is relatively new part of the WordPress, and so far, very few themes are made to use REST API.
If you need a mobile app that will have own interface ( the theme is not used for the interface), that app can be made to use REST API, and that has nothing to do with the theme. The app can also be a theme, and it can be made not to use REST API.
It all depends on your specifications and what you want to do and how. WordPress can be used in many ways, and any task can be done in more ways than one. Anything can be made to use REST API or to work without REST API. API returns result only, the app (or theme) needs to render those results. The main point in using API is to separate the server side from the front end rending.
You should learn more about WP REST API, understand better what it does and how it is used before deciding on using it: WP REST API Documentation and REST API Handbook, and you need to better formulate your project before deciding one way or the other.