It is. I think that's one way to define it. I have just a couple of points to make. Not all processed foods would have added sodium, sugars or saturated fats. Also, some types of processing actually contribute to food safety. For example, milk would be considered a processed product because pasteurization is a process.
Those are some of the challenges around saying there should be no processing at all. It would potentially not necessarily capture all of the products that you might want to consider. It might actually inadvertently capture some other products as well.