Fake costumes only add to your pet's transformation count; it doesn't change the pet itself. For example, if I used a fake coral costume on my anime Kaala, my Kaala would still be anime, but under her transformations stats, it would say that she was once a Coral Kaala.
While it doesn't change your pet, you can change your pet to that color if you have enough Drew vouchers because it counted as part of their transformations.
Hopefully this all makes sense. Short ways, it doesn't change your pet, just adds to their count.