Will Dart support the use of existing JavaScript libraries?

There is now a new simpler way https://pub.dartlang.org/packages/js (currently version 0.6.0-beta.6)

Make JS classes and functions available to Dart like:

@JS("JSON.stringify")
external String stringify(obj);

@JS('google.maps')
library maps;

// Invokes the JavaScript getter `google.maps.map`.
external Map get map;

// `new Map` invokes JavaScript `new google.maps.Map(location)`
@JS()
class Map {
  external Map(Location location);
  external Location getLocation();
}

// `new Location(...)` invokes JavaScript `new google.maps.LatLng(...)`
//
// We recommend against using custom JavaScript names whenever
// possible. It is easier for users if the JavaScript names and Dart names
// are consistent.
@JS("LatLng")
class Location {
  external Location(num lat, num lng);
}

for more see the readme of the package

You will not be able to call javascript directly from dart code. The native directive is reserved for the core libraries of dartc (dart:core, dart:dom, dart:html, dart:json, etc), which itself compiles to javascript.

The answer is now Yes! Dart now ships a JS-interop library to use existing JavaScript code with your Dart app. Learn more here: https://www.dartlang.org/articles/js-dart-interop/

There is also a dart:js library. And here is an article explaining how to use this library for interoperating with JavaScript.