No, and Yes!
Ok, so it depends what you mean by desktop app. If you mean something that compiles Dart code to a native .exe or binary, and has bindings for things like QT, Swing or WPF, then no, you can't build a "desktop app" with Dart.
On the other hand, if your definition of a desktop app is an app that can be installed, has it's own icon on the desktop, runs independently of a web browser, then the answer is definately Yes - using Chrome Packaged Apps.
Chrome Packaged Apps allow you to use modern web technologies to write an offline/online application in HTML, CSS, Dart/JavaScript. They are hosted in a Chrome process, but not within the Chrome browser itself. They get access to a wider range of APIs, such as USB, Serial ports, filesystem etc.. You can install chrome packaged apps for Win / Mac / Linux (from the same source-code). They have their own "skin", ie, they aren't visibly running inside a web browser. This gives you a "native" feel to the app, whilst still being able to write the app using web technologies.
(The book, Dart in Action has a chapter dedicated to using Dart to build an "offline first" application, and installing it in Chrome. The Chrome Package App is the next step on from this).
Want a demo... check
out a recent blog post which contains a few video clips, some instructions, and a link to the
Chrome Packaged Apps developer documentation.