There are also two alternatives: https://apphub.io/ and https://microsoft.github.io/code-push/. Works for me in the real app very well, even in a synchronous mode in some cases.
With CodePush, AppHub, and this, it would be nice to have the community converge on a shared auto-updating client. Perhaps down the road we could see this functionality integrated into React Native itself.
[1] https://github.com/AppHubPlatform/apphub-ios
[2] http://docs.apphub.io/docs/self-hosting
Disclosure: I created AppHub