You can use Sencha as a framework to build stuff + using it's native packager in order to wrap it up to a file mobile devices can install (.apk on Android for example), but it doesn't support push notifications for now, hope that it will support it for both Android+iOS in the future.
You can use PhoneGap as a packager, on top of the Sencha framework. That way, you can integrate UrbanAirship, for it uses plugins that the native Sencha packager can't work with.
The integration of Sencha+PhoneGap isn't easy as JQM (in the dreamweaver it's Plug&Play), but it's possible.
Regarding working UrbanAirship, what I just wrote theoretically should work, and I'm on the way to make it work, I hope so I can't tell you from my own experience that it's working for me.
Hope that helped.