As per the title:
If a reconstructive surgeon removes a rib (to repair some other part of the body) could that rib grow back?
A whole rib? No.
Small pieces of bone are used as grafts, such as in spinal fusion operations, and do fuse with other bone. But that’s not really regeneration. The result isn’t that strong and stable either, since metal caging is necessary to keep the spine stiff afterward.
Skin grows back, although only if the damage isn’t too great, but the rest of the body isn’t designed to do so.