The southern sun is tough on any material, plus most fiberglass roofs are painted and the paints fades/chalks in intense sun. I'd have it under a roof if practical, but do not consider it a "must". All our Rvs sat in Florida sun (but partially shaded) when not in use and didn't suffer too badly. The fiberglass roof coach needed to have the roof repainted after about 10 years, and I did that myself in one afternoon, using a brush and Dicor Fiberglass Roof paint.
Former owner of 2004 American Tradition and several other RVs
Home is West Palm Beach, FL