Ember-Cli is just the command line toolchain that the Ember community is "blessing", so it's really just a different way of building the ember app.
I'm actually using Ember-Cli with ASP.NET MVC and WebApi. Essentially what I'm doing is using EmberCLI to output an index.html file (ember new myapp
sets up a project to do this by default), and then having my MVC app route to an /App url, where the controller returns a View("~/whateverdirectory/myapp/dist/index.html");
Razor doesn't care that the view you return isn't a .cshtml file, so this works fine, particularly if you're using Ember to control the whole page. This way you can use the standard authentication in ASP.NET, and then when the user is logged in, send them to the App controller's index route through MVC, and serve them the Ember app.
Update 8/18/2015
I've added some sample code on github.
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