CodePush will also be integrated into Mobile Center, so that you can also making CodePush a part of your CI process.
We are also working on adding support for Authentication, storage, testing and Push notifications.
[I am the PM on CodePush and React Native Mobile Center stuff]
You should be able to use Mobile Center and CodePush separately today. We are planning to incrementally roll out a backward compatible solution over the next 2 months.
That seems like a no-brainer if you are supporting React Native based apps.
Also, I didn't see any support for platform native Notification APIs for React Native. The current notification service is for pure-JS / Cordova[1]
[0] https://microsoft.github.io/code-push/
[1] https://azure.github.io/azure-mobile-apps-js-client/