you could do it the way they did before accelerated desktop compositing.
-Window with no frame (no problem!)
-Drag window to move (events, no problem!)
-On move, capture background and composite within application (Uhm.. python? :s I'm sure desktop capturing has been discussed before in the forums.)
That said, capturing background isn't fast, so you shouldn't update each frame. This means that the captured background will not reflect changes until you move the window forcing an update.