The statement is True. Protists are a diverse group of eukaryotic microorganisms, which means they possess a membrane-bound nucleus. This characteristic is one of the defining features of eukaryotic cells, differentiating them from prokaryotic cells, which do not have a nucleus. The presence of a nucleus allows protists to compartmentalize their genetic material and perform various cellular functions more efficiently. Thus, the defining trait of protists includes having a well-structured cellular organization, including organelles enclosed within membranes.