I don't want to wait anymore and would like to use a polymer element written in dart right away.
The problem is that I want to use it in an already existing app, that's running on JavaScript.
Can I just compile my polymer elements to JavaScript, include the whole thing in my current app, and use my <awesome-element> tags?
No, you have to build a Dart app to use Dart Polymer elements. You can include JavaScript in a Dart/PolymerDart application.