I wouldn't recommend it in my opinion. Food has a BIG impact on skin and coat. Feeding a high quality food will usually eliminate skin problems pretty quickly.
The bad ingredients in pro plan are: corn gluten meal, ground yellow corn, and corn bran. That is a lot of corn! It can be difficult to digest and is a very common food allergy in dogs which frequently causes things like flaky skin.
Try to pick a food that doesn't contain corn or meat by-products. If Luna has a sensitive stomach, you might want to try lamb & rice flavor food. A really high quality food can do wonders for a dog!