Could a postoperative staph infection cause calcifications to deposit in my body?

Yes. Calcifications can be attributed to many causes. Any time there is a foreign body within the body, the body's immune system tries to control it by directly killing the foreign body, surrounding & forming a barrier around it, and "remembering" it in the event of a repeat exposure in the future. Part of the healing process may involve forming a calcification, a kind of "internal scar.".