Is the Android desktop screen (on any version) a Dalvik executable?
What you describe as "desktop", and the screenshot shows, is called by different names. Mostly it listens on the names Launcher and Homescreen, depending on the aspect referred to. And yes, it's an app that ships with its own .apk file, as all its "replacements" (e.g. Apex Launcher, GoLauncher, or Holo Launcher – to name some) do.