False. I never tested just how far away you have to be, but I decided to try it out on Hyrule Temple just to see if the range was infinite. I had Peach on one end of Hyrule (the big flat part on top, not the topmost platform) and placed the opponent on the other side.Peach's. No matter where you go you will get hit.
I activated the Final Smash. The opponent neither fell asleep nor did they take any damage. So the range is not infinite.