No. Wolverine doesn't seem to be able to lend his healing powers out.
Angel however has healing blood which manifests as a healing factor for him, and he can use it to heal wounds of others--I believe it went so far as to cure a young girl's cancer.
Also, Elixer (I think that's his name), Josh of the new New Mutants power is primarily healing, and he's an Omega level too--although he hasn't completely tapped into it yet. He could probably heal Prof. X's back, and Cyclops' brain trauma that keeps him from fully controlling his powers (but there is the issue of a subconscious battle, etc.).
Rogue used her powers to copy Wolverine's healing factor. I don't recall the cartoon too well, I remember at one point they used his healing ability to create antibodies for a disease of some sort.
I suppose Magneto could manipulate Jugg's armor a bit, until Juggs started up some mystical shit, then Magento's power would probably be ineffectual.
He didn't ask if Prof. X could absorb Wolverine's powers, he had a simpe question to which I gave him an answer. From a newbie point of view, it would have looked like Wolverine had used his healing factor on another person in the first movie, and I think that's where his question came from. In the comic book world, I think anything is possible. Magneto/Xorn cured him for awhile, and Charles was fairly happy with that, but I don't think he'd ever go out of his way to cure himself, it reminds him of his greatest defeat and tethers him to his peaceful humanitarian dream.