At the end of "The Wolverine" Wolverine got his claws cut off, but the bone claws still remained along with his adamantium skeleton. Will his bone claws therefore get coated with adamantium as time passes?
If this is solely for movie cannon, the only way to know is to wait till the next movie and see what script writers have wolvie snikt-ing.
If comic cannon, there are conflicting opinions "officially" it would heal back just as his bones as it is Adamantium Beta (though I would have thought at a slower rate as it is known to retard his healing factor a bit), yet when Magneto removed the Adamantium from wolvie it did not heal back. Whether there has been an explanation for this confliction or not I dont know