This is not advised. The soap can hurt the animals eyes. If you are careful not to get any mild dish soap in the eyes, you can use it. Cat shampoo is advised because it is very mild and wont hurt the animal.
There are many dish soaps that have long lasting suds. They include: Joy Dishwashing Soap Palmolive Dawn Liquid Dish Soaps Ivory Dish Soap Natural Home Dish Soap Ajax Liquid Dish Soaps Mandarin Coriander Dishwashing Liquid J.R. Watkins Natural Liquid Dish Soaps Shaklee Dish Soap