AngularJS controllers are NOT compatible with AngularDart.
I haven't tried but what could possibly work is that AngularDart and AngularJS work in the same application when they each have their own root element (ng-app) and one root is not a child of the other.
You can use Dart-js-interop to call JavaScript functions. But your service can not be used with dependency injection. You could build a Dart wrapper that does the Dart-js-interop and register the wrapper in DI.
I would expect it to get complicated when the JS service itself needs DI (or any other functionality from AngularJS) for its initialization or processing. I don't know AngularJS or RestAngular but I would rather consider porting RestAngular to Dart.