Yes, Methadone is stated to possess the common Opioid effect in that it should reduce the coughing reflex. I am unsure how it compares to something like Morphine, though I do know that Methadone can be prescribed as a painkiller when antitussive effect is also required.
I have no idea i havent had it. It was available here until a few years ago but now its off the market i think. It was available in concentrated drop form. It also had ephedrine in it so that part sucks