To the best of my knowledge, yes, he did recover his rings, and wore then on new, dragon-like hands he grew for himself. He tried to cleanse the world of technology, but was infected with a techno organic virus, then transformed by the Heart of Darkness (the thingy he'd been using to perpetrate his plan) into a lowly janitor, while everyone believed he was dead.
He resurfaced near the beginning of Vol 3 of the title, with his newest creation, the Dragon of Heaven, a massive dragon-shaped warcraft. He did not have his original rings now - instead he had control rings which he used to work the Dragon. Blah blah blah, Iron Man wins fight, Dragon is destroyed, Mandarin apparently dies when it goes down in flames.
Just recently, it was revealed that the Mandarin left behind a son, who's a crimelord of some kind or another somewhere (sorry, but I just honestly did care enough about the story to remember stuff about it... /

- who is presented with his father's hands, complete with rings, which are stated to have been found in the wreckage of the Dragon of Heaven. The rings are later shown to have powers like the Mandarin's original rings. So... yeah, I dunno. Make of it what you will.