In Rhodium, yes. Never heard of black Rhodium. You could ask these guys. http://www.razoremporium.com
I think the handle of some later SA's is aluminum, not typical brass, but could be mistaken. Whether that makes any difference in plating?
I think Gorgo's right about the aluminum handle. Aluminum can be plated but I think it's a little tricky. I really like the look of that black rhodium plating. You'd have one beautiful and unique razor if you could find someone who can pull it off.
I think the only problem might be the coating on the handle which from what I've read is a "textured acrylic resin" on the models that use brass, I've never seen one of the aluminum handled razors. I don't think the resin can be removed and then replaced, so could it(the resin) be put into the plating solution with no ill effects to either the coating or the plating? Other than that I don't see why you couldn't replate it in Rhodium or anything else that strikes your fancy. It would be a Fantstic looking razor thats or sure!!
Well, I can tell you from experience (luckily with a late model Super Speed, not a Super Adjustable) that the gallon jug of degreaser from Walmart auto dept. will remove that black coating very quickly, but only because the sodium hydroxide will also totally dissolve any aluminum that soaks in it. All I was left with was the nickel plated head, the knob and the rod that connected them. Moral of the story: I have no idea how to remove the black coating that wouldn't wreck the tread on the grip (sanding it off leaves a very smooth barrel...again, don't ask me how I know) but you'd have to do that successfully in order to plate.