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.
I am currently looking to add push notifications to one of our Touch 2 apps and also going to try PhoneGap and Urban Airship. First step will be wrapping with PhoneGap and then trying to integrate UA. I'll let everyone know my progress and struggles.
I've not played with Urban Airship but I've successfully integrated Pushwoosh with Sencha Touch and PhoneGap. Push notifications are working a charm on Android, there's even a full guide on their website.