Absolutely. Armed only with the knowledge of JavaScript, React, JSX; you can jump head forward into Android/iOS development.
The main difference between traditional React.js and React Native is the rendering context. Instead of rendering DOM elements, React Native renders native UI views.
You're sort of correct in assuming that it converts JavaScript to native code. To put it more precisely, picking it up from Facebook's React Native page:
All operations between the JavaScript application code and the native platform are performed asynchronously, and the native modules can also make use of additional threads as well. This means we can decode images off of the main thread, save to disk in the background, measure text and compute layouts without blocking the UI, and more. As a result, React Native apps are naturally fluid and responsive. The communication is also fully serializable, which allows us to leverage Chrome Developer Tools to debug the JavaScript while running the complete app, either in the simulator or on a physical device.
React Native has its own JavaScript engine running on a single thread, which asynchronously communicates with the native platform; this communication "converts" React Native components, to the native mobile OS components; and from there on the native platform has got your back with its multi threaded goodness, for performing further native operations, from the way I understand it.
I'm still in the phase of getting my feet wet with React Native. But from what I have read so far, ideally you will find everything to build a mobile app with React Native; granted you would have to dig in the docs to learn about the corresponding iOS/Android react native components. React Native is growing at a rapid, rapid pace. For those native components, for which the counterpart React Native components do not yet exist; as @sriraman has mentioned it, the community (along with Facebook) is doing a phenomenal job in quickly closing this gap.