Yes Gatorade is good to drink when you have food poisoning since the Gatorade is meant to keep people hydrated especially during sports.
Pedialyte is another good drink to drink when you have the flu or food poisoning since the Pedialyte can help replace lost electrolytes in your body.
Even drinking water or tea is better than drinking nothing and as long as you replace lost fluids and stay hydrated when you have poisoning you'll be okay.
The food poisoning should go away within 2 to 3 days and if not you should see a doctor.