Is it safe to just copy the Xcode 4.4 app from a machine to another or does the Mac App Store download an installer, rather than just a bundled app, and some Xcode 4.4 pieces get installed somewhere in the system?
Xcode, from version 4.3 on, is a single app and self-contained. Source :
The command line tools, which are stored elsewhere on the filesystem, are an optional download which you can install separately.
When copied over manually, the App Store will recognise Xcode.app's presence and change the badge for the application in your "Purchases" from "install" to "installed".