No, please don't. You can by special spray shampoos that you can use on your dog between baths. Pet Head (the pet version of bed head), makes these, you just spray on, avoiding the face, and towel off. Just make sure your dog isn't sensitive to scents and perfumes, since most of Pet Head's products have a strong scent.
If you are referring to a real dog, no, their skin pH is different from humans and you could cause a problem for your pet. If you are referring to a stuffed animal, I don't think the dry shampoo would hurt it, but it seems an expensive way to clean it. There are commercial dry spot removers that you can use to spot clean fabrics that are cheaper than pricey hair dry shampoo.
I wouldn't recommend it. Dry shampoo contains things that any living creature should probably not ingest, and well, dogs lick themselves.
If it's for the stuffed animal then, sure, why not?