No. The pH and characteristics of pets' skin are different from ours, therefore they need specific products. The pH value of a dog's skin is neuter and varies between 6.2 and 8.6, depending on the part of the body.
Additionally, pH can influence the electrostatic forces that ward off bacteria and the activities of anti-batterical enzymes produced on its surface, essential to the skin's ecosystem.
There are different types of shampoo for the different types of skin and fur of cats and dogs. You also must beware of shampoo fragrances, as some of them may not be tolerated by your pet.