As long as you include your mandatory dart lines in your html files:
<script type="application/dart" src="fileName.dart"></script>
<script src="packages/browser/dart.js"></script>
you should be able add the dart replacement code and compile it. This way you may be able to start converting over bit by bit. To the best of my knowledge there is no way to call dart code from JavaScript though.
Now that I have a little more time, let me expound a bit. Since Dart is a relatively new language, along with the fact that it doesn't so much add anything to the JavaScript language, there isn't a lot of incentive for Oracle to add cross-compatibility with Dart. Though the two languages may not so much be cross-compatible, they can both coexist together and have a more one way relationship.
As long as you are calling your dart code directly from your html files or from other dart functions, you can at least start the process of integrating dart into your site. Then as time allows, you should be able to start the long process of updating your JavaScript to dart, if that is the direction you decide to take.