We're working on a Linux port for use server-side but that's not to say our current framework is not headless. We developed this branch to be completely independent of any windowing systems (and have even coaxed Flash and Silverlight to render correctly in such an environment)-- check out our HelloAwesomium sample in the SDK, it runs straight from the command-line and outputs a JPEG.
If you only run on Windows or OS X, it's windowless, but it's not headless.
Headless means something running on a command-line console, and you can't run either of those operating systems that way.