Using ServiceWorker in Cordova

We have been happily developing our app using Service Workers because of the ease of building an offline app.

It's registered in the usual way:

navigator.serviceWorker.register( "./worker.js" ).then( function () {
  console.log( "woohoo!" );
}, function ( err ) {
  console.log( "oh noes", err );
});

And it is actually quite simple:

self.addEventListener( "install", function () {
    console.log( "yay" );
});

It works fine while developing in the desktop browser, behind a web server.

But is there a way to use it while in Cordova/Crosswalk, as they use the file protocol?