Maybe. But we don’t recommend it. A few sips of Gatorade are perfectly safe for your dog, but water is the only fluid your dog needs to stay hydrated.
It may help your dog somewhat to have a few sips of Gatorade after a bout of diarrhea, but Pedialyte is probably a better choice. Gatorade also contains added sugar and sodium, which undermine any benefits Gatorade might provide.