Sorry to report Hardee's does not use a dedicated fryer for its fries. Even though the regular fries do not have any gluten-containing ingredients, it's highly likely use of the same oil for onion rings and other gluten-containing menu items would result in cross contamination.
I still think it would be a great idea for the company to make the move to dedicated fryers, especially since they have reached out to the gluten-free community. I am trying to get in touch with a company rep to talk about that possibility.
Meanwhile, the burger, the breakfast bowl, and the salad, as well as a few other items, are gluten free. You can download special gluten-free coupons at http://www.hardees.com/menu/indulge that will give you a free Coke or Dasani bottled water with the purchase of the breakfast bowl and a free salad with the purchase of a burger and a Coke.
One positive way to look at this is that the salad is better for you than the fries anyway.
Will let you know if I make any progress on the dedicated fryer.