It may help some, I have shipped them in boxes and not in boxes or bags and really not noticed much difference, Key things to remember and think about. Go straight home, make you fish stop your last stop, Keep the temp as stable as possible, Don't leave in a heated car, don't leave them in a car with AC on high., Try if possible to bring them home with one or two fish in a bag, the more fish in a bag the more ammonia and the faster the water will spoil. If they have oxygen to put in the bag get it! even if only ten minutes away, reason being, you never know what might come up, (flat tire, detour, accident etc.) This will give you extra time if something happens and you get delayed on the trip home.
I like having a cooler with me when I'm buying fish, This keeps them insulated, keeps them for rolling around and possibly puncturing a whole in the bag, and if for some reason the bag does get a hole in it, You can pour the fish in the cooler and keep them there until you get home. However I don't recommend starting off putting them in the cooler with out bags. that is just a backup plan in case something happens, the bags have the oxygen in them and they are cushions that will help prevent injuries.