I assume this is being proposed by an otolaryngologist (Ear Nose Throat specialist) because you have a paralyzed vocal cord? My right cord is paralyzed but the position is good enough for speech and I don't have any breathing or swallowing issues. I've been told that the use of the injection (or the build up procedure) can be helpful to those with certain types of impacts from vocal cord paralysis. The second thing you mention - the wedge - is not so much to move the broken cord over as to build up a sort of extension to where it currently lies fixed in position. The Mayo Clinic website has a very good summary of these two procedures and what they do. I'm not sure if I am allowed to post a link here, but you can search for "vocal cord" within the Mayo Clinic site to find the educational page about vocal cord paralysis treatments.
I confess I have not looked for more of your posts so I will answer your question. Yes I have had it done. 2Xs. Yes it works along with speech therapy it is wonderful. Radiesse is a filler that people use to plump up things like lips. It also plumps up a vocal cord moving it more midline.
After the injection (mine was done under a local and I was "out") you will not be able to speak for 5 to 7 days and I am dead serious nothing unless it is life threatning my ENT said. If you speak the Radiesse will squirt out of the injection site so you must heal before you speak.
Follow my old posts in the archives about speech therapy there is tons to look at and help is there.