Is it possible to use NativeDroid as the UI of an ionic application?
Not sure. But it runs counter to what Ionic is. One of the primary things that Ionic offers is its UI library. Why would you replace it?
Also, that library is built atop JQM, so you have that library (and jQuery) to fold into your app. If you want to go with that solution, the I would suggest just using the Cordova layer directly, build your app atop that UI stack and forgo anything Ionic.