I'd recon that (in extremis) any aircraft with reverse thrust could "power back". As to whether or not is allowed by the AOM (for the good reasons mentioned earlier) or God's Gods of Aviation (the local airport managers) is a different matter. Going back a few years, an Aeroflot IL62 did it's own "pushback" at LHR (there was some dispute with the Soviets) and they were refused ground handling.
However, it's amazing how quickly the rules change when you are blocking a stand which is required!