yes, you can definitely add piping to the areas. I would baste them to the main fabric first, before adding any finishing elements like lining or facing pieces. As long as you have one area, such as the bottom of the bodice that remains open, you should be able to flip the bodice right side out. Usually with a zipper, that same seam on the lining remains open. After the bodice is flipped right side out, you hand sew the lining to the sides of the zipper on the inside. It really doesn’t matter if it’s a concealed or visible zipper or has piping or does not have piping. The method is usually the same. If it’s a little confusing, you can watch this example I do of adding a lining to an area with an invisible zipper, it’s near the end. It may not be exactly like yours but maybe help a little. https://www.professorpincushion.com/professorpincushion/invisible-zipper-with-a-lining/