Outside the Lines: Adamantium Bones
Live Science poses the question: Could you really have adamantium bones like Wolverine? I can't say they actually answer it -- adamantium doesn't exist, so I'm pretty sure the answer is "no" -- but they do talk about a few creatures in nature that contain metal:
The idea that metal can be bonded or combined with organic tissue is not as science-fictional as it sounds. For example, the mandibles of leaf-cutter ants and locusts are peppered with zinc, making them stronger and more durable. Some marine worms have copper in the protein matrix that makes up their jaws.
And while you can't actually cover your skeleton in alloys, science is now able inject new bone into your body by shooting it into you with a syringe.