And so I went out to develop an app for the DevTeach (http://www.devteach.com) conference (in which I am speaking and running a workshop next month). And here I created quite a simple app in a couple of days. And it runs on both Android and iOS.
Overall, I am quite pleasantly surprised by the versatility of React Native and I saved quite a lot of time in testing my UI as I don't have to redeploy the app every time I have an UI change - pressing Cmd-R reloads your app.