I wonder if it is possible the any auto tune might make things even worse if you are not close to the correct note? If it guesses the wrong note, you might end up even further from the intended result.
I'm not sure how auto tune works. If it is programmed with the correct tune, then it might be able to correct whatever you do. But if it only corrects to the nearest likely note, then you would be in trouble if you get it completely wrong and are not just a little flat.