cpalm, the short answer is no. A closed loop is not essential. What is essential is good flow. Depending on the size of your tank, the sump flow is enough.
You can use powerheads instead in the display tank to improve water circulation. They are cheap enough and are a very easy solution to water flow. I have 3 in my 125gal tank placed in different parts of the tank and pointed in such a way there's no dead spot (or area without water movement) inside the tank.
Does that answer your question?