I mean... It's probable that Wolverine has AIDS or some other diseases like that in his body. According to his Bio, he's immune to diseases. But he could very well be a carrier. The problem with Wolverine is the same problem I have with many other characters. Their powers can't be logically explained and measured. And even if you could, some other writer and artist will come and ret-con the whole thing and change it to "make more sense".
I mean think about the regenerating factor. He grew back from ONE cell. What would happen if more than 2 cells (separate by a great distance) survived? Would they grow back TWO wolverines? Would he grow back from just one and the other then... erm no? In one of the Xavier protocol to kill off his own X-men should the need arise he reccommends choppin' off his head. But if he can grow back from one cell (what's the point??). I'll tell you the problem. Different writers... They all come in and fuck the whole shit up.
Once I saw Wolvie fighting Hulk, when I saw a weird thing. He cut the Hulk skin. I told my friend (the comic owner) how could that be?? And he was like well duh, that Adamantium in his bones. And I was like "But this is a post-Magneto incident" "He has just his BONE claws (no Adamantium plating)". And my friend said (without a pause) yeah well, he lived so long with his Adamantium in his body that his bone structure absorbed some of the properties of the metal thus becoming indestructible (he used another lingo but it's the same thing). And I was like... Ok... Then it hit me. My friend was the same as the new writer taking over his predecessor. Just taking the shit he wanted/assumed he wanted to keep and re-work everything else.
Did you know in his original appereance in Hulk, Wolvie was a regular hit man with ADAMANTIUM GLOVES that had some claws. Neither the claws or the regeneration/healing factor were part of his character just yet. Oh and supposedly (even tho' his face was covered by his mask) he was supposed to be young looking and almost hairless. He was later changed when the character proved to be popular.