A hammer action drill and impact driver work in a completely different way. Hammer action produces vibrations in the longitudinal axis of the drill whilst an impact driver produces vibrations in the rotary axis. I am not aware that any of the major manufacturers produce such a beast but I may be wrong. It sounds like a bit of a mash up and because you preceded your description with the word "cheap" I am inclined to think it probably is. Nevertheless post a link I would be interested to see such a device.

Richard