Shadow biotech is pretty strong stuff.
Morden does have an implant in his brain that allows the Shadows to speak directly to him. It is also suggested that this implant regulates his emotions to a degree. Full details on the implant are in this question about Morden's choices. It's possible, but unlikely given it's small size, that there are healing functions attached to it.
That said, nothing ever suggests he has ever been enhanced to a radical degree, except that cocky invincible smile.
Shadow biotech is capable of breaking down other biomass and reassembling it for whatever purposes they deem fit - this is witnessed in The Passing of the Technomages, the last book, Invoking Darkness. Healing and reconstructing biomass would be child's play at that point. Given the entirety of Morden's comment on the matter - "the flesh will serve" - it's likely the Shadows are putting him through an accelerated healing process, one that is not terribly pleasant.