We've discussed Wolverine regenerating his body after nuclear explosions, but his adamantium-laced skeleton was left in tact afterwards.
After Magneto ripped the adamantium from his body, Wolverine has had his bone claws broken and they grew back due to his healing factor.
In The Age of Apocalypse, Cyclops was able to break adamantium with his optic blasts.
Assuming his adamantium covered skeleton was broken by something other than the Muramasa Blade (which inflicts wounds which do not heal), would his body regenerate the adamantium covering as well?