The bones are coated in adamantium if memory serves right so presumably if you cut through his bone it would just regrow normal bone then everything else. Wolverine has had the adamantium ripped out before and while excruciating he did heal back up, he has also been disintegrated down to just his adamantium skeleton at least once before which seems to have effectively killed him but that was also the days of future past storyline so who knows maybe he could’ve regenerated from his eyes, but also there’s a version of wolverine who’s down to a stump on one arm but then again Apocalypse was involved so who knows what was going on with that.

So in summary, data inculclusive.