As a maintainer of a popular and actively developed open source project, I would totally use the app to respond to issues and pull requests if it were usable. Unfortunately, the app is a dumpster fire, so I just use github.com.
If you do use android for development, you wouldn't need a github app to push your code to github. You would need a git app, and several great ones exist.
Is it really that difficult to get push notifications for pull requests, issues, and my homepage news feed?
I don't know what it's built with but it's not native in the least, it looks like some awful PhoneGap monstrosity.