The reference states a cockroach is a harbinger of dirt and najis (implying impurity) but does not explicitly state it is najis. This suggests an association with impurity, but not definitive impurity itself. Therefore, whether a cockroach is considered najis depends on specific interpretations within different Islamic schools of thought.
More information is needed to provide a definitive "yes" or "no" answer, as interpretations on what constitutes najis can vary. It depends on the specific Islamic school of thought being followed.
