Is it reasonable to assume that a power cord could make a difference in my system at this price point?
Sure, but remember, different is not always better. I do not have much experience with current cords in your price range, so I will defer to others who are more experienced with your quest.
From my experiences years ago, I was once a skeptic too, I didn't really find power cords to have much effect on the lower priced cords in lower priced, less resolving systems. It wasn't until I tried better cords in more resolving systems that I found the true benefits of having upgraded power cords.