This question comes up often. ROP requires HACCP. No ROP, no HACCP.
First, a common item exclusion for a different reason. All acid foods pH ≤ 4.2 are non-TCS. As a non-TCS food, no HACCP. So, cold bagging dressings, acidic sauces, etc does not require HACCP because its non-TCS.
What about cold bagging TCS foods, like proteins? The answer from FDA is no vacuum or removal of air, not ROP, no HACCP. Read their interpretation carefully.