Because copper is a metal, it is non-porous and will not stain in the traditional sense of the word.  Copper will oxidize and patina which is a chemical change that produces a different color in the metal.  It oxidizes rapidly and will move toward a deep, weathered brown color.  Almost anything that comes in contact with it will oxidize it to some degree; in essence, it’s a living finish that constantly changes.  It can be maintained with or without a patina.  A full patina does take some time to develop ( typically, a year or more).