This has been the question since the day I saw Facebook unveil the new Facebook Home suite of apps. Workmate of mine (@stevelarkin_) might have found the answer on good-ol' StackOverflow!
http://stackoverflow.com/questions/13346111/draw-overlay-in-android-system-wide
Basically, you are able to spawn a service which draws directly on to the Android System's WindowManager by adding a new subview on top of everything. It requires some special Android permissions that the user can agree to during the install. Code example on the link.
Can't help but deeply appreciate the flexibility of Android.