Unless other browsers support it via browser plugins, it could turn out to be a dead end, Google is betting on mutiple horses here because themselves cannot predict this.
Its also possible to compile Dart to Js and use it as an improved language for web development.
But the JS VMs are already very fast these days, so being the performance of Js VMs acceptable there is not much reason to go from Js to Dart.
I have the impression that Ecmascript 6 and Web standards like components, templates, imports and shadow dom are the future of the web, and not an alternative language.
All browsers are investing very heavily on that, in 2015 we should probably start having the first Ecmascript 6 compliant browsers.
ES6 seems to be the backwards compatible path of least resistance going forward, and that is the path that usually succeeds.