@TheRanged Only if the metal was adamanttium would this work for the whole skeleton, and you need a mutant with extraordinary regenerative powers for this to work.
We routinely perform the substitution of bones for solid metal ones now, at least in part, with Hip Replacements. And we routinely implant metal with heart pacemakers.
Do you mean whole skeleton, or just the odd bone here and there as the whimsy takes us?
More seriously - A significant proportion of the public have hypersensitivity to chromium, nickel and cobalt. GvH rejection due to immunological rejection has been conjectured, but not yet clinically proven. Metal sensitivity, and delayed onset of dermatitis, vasculitis and urticaria have been demonstrated to occur and are linked to implant degradation products, but not to cause failure of the implant.
There are many other considerations to take into account when contemplating the replacement of bone with metal.Mechanical considerations, for instance.Bone is strong, rigid and yet pretty light for its size - replacing such material with metal would significantly change the stress on and amount of work carried out by muscles and tendons, and not in a good way. Bone also is a reservoir for bone marrow, which in turn acts as repository for all sorts of good things, such as blood replenishment, stem cell generation, which aids in cell repair, and our bodily defences, with a pool of cells involved in our immunological system.
Replacing such reservoirs with solid metal would again be a pretty bad idea.