As you can see your answers here will really depend on how you define sway. My trailer occasionally moves to the side a little bit as the roads are not perfectly smooth. I think this is a normal condition as the trailer is on a ball and can therefore move a bit as the road surface changes.
In my first year of towing I worried about the movement and wondered if it was sway. Basically the people on here told me it sounded normal and I would absolutely know if the trailer started swaying. Now ten years later and I don't even notice the small movements of the trailer any more than I notice that I have to make small corrections in my steering to keep my vehicle on the road.