Probably not, because the difference may be whether or not it's scented with something that is harmful to birds...Bird-specific cleaners don't have any scent, nor anything added that's caustic. A cleaner used to clean-up dog messes isn't going to be made to be used inside a bird's cage. Not good...
Just make-up a mixture of water and white-vinegar. It's safe, it works well, and it won't make your bird sick or worse...