Will a mazda-mx5 automatic drift the same as a manual?

No, it will not be the same. There are multiple ways to initiate a drift sequence in a car, and you would use different styles to achieve different "stunts". Search for the "Drift Bible" on YouTube. While a drift can be initiated by upsetting the weight and balance of the car, the more advanced drifting techniques involve instantaneous gearing changes and clutch manipulation to shift weight and break the rear wheels loose.