Using a dish soap can have benefits. The grease cutting properties will remove the waxy layer of the fleas, will dehydrate them, and they die from dehydration. You have to leave it on them about 5 - 10 min for this to work, about the same time a flea shampoo is left on. Just be careful about getting dish soap in eyes, as it can cause pretty severe ulcers. Again they grease cutting properties removes the lubricant in the eye, and the blinking that follows from irritation can rub ulcers on the cornea.
I don't use Joy, I use Dawn when my girl is especially grubby, but always follow it with a conditioning rinse, dont want to dry her skin out.