No, its not. The pH of human shampoo is not right for a dog and can cause skin irritation, dry skin, and even hair loss. Baby shampoos that should be mild are the worst, actually, for use on a dog. Most dandruff shampoos are actually harsh on human skin, so it is not something I would suggest for your dog.
If you want to bathe your dog, I would suggest using a good quality dog shampoo. My personal favorite is HyLyte because it smells very tropical, like coconut, and has essential fatty acids within the shampoo to moisturize the skin and coat. Your veterinarian may carry this if you are interested. Your veterinarian also may carry a line of prescription shampoos that are aimed toward dogs with allergies. Look into it.
Your dog's coat is managed by the essensial fatty acids linoleic acid and linolenic acid. Using a diet supplement like Derm Caps (a capsule once or twice a day) or ProDerm (a powder you sprinkle over your dog's food twice a day) can also help with the skin. These two products are great and contain those essential fatty acids, as well as omega fatty acids. ProDerm also has some other nutrient additives. Either way, using a coat enhancing/skin nurishing supplement may help out - just make sure they are canine specific and are more natural so as not to make your dog's allergies worse.
BTW, if your dog has atopy (which is inhaled allergens) talk to your vet about Atopica, a cyclosporin medication that is wonderful! If your dog has food allergies, try venison or duck or rabbit based diets, or even a prescription diet like z/d where the proteins that your dog most likely is allergic to are so small they do not cause a reaction. If your dog has flea allergies, try this great new product called Comfortis - a pill that lasts for 1 month, and starts killing fleas within 4 hours. It is a miracle worker. You could also try a veterinary dermatologist for allergy testing and have desensitization serum produced for your dog - so you would give a shot of what actually causes the reaction within your dog in small amounts to make your dog 'less' allergic to them. If you are using a plastic bowl for food and/or water, change to metal bowls as dogs can be allergic to the plastic. If your dog has environmental allergies, wipe his feet everytime he comes in from the outdoors, try benadryl or if this no longer works, there is also a drug called Temeril P that is lower steroids than Prednisone but is effective. There are always paths to be found. If you want any information on the products or have any questions about allergies, email me.