No, socioeconomic status is not unrelated to excellence in education, because wealthy children tend to do better in school. Often, richer people have a better work ethic than poorer people. Additionally, richer people can afford to put their children in extracurricular activities that poor people cannot afford. Extra opportunities give richer students an advantage.
Having a status in high society affords children better education opportunities, and tutors that make a severe impact on their success. Status is not everything however. Some people are just naturally gifted to learn. Though, children of rich families usually go on to great success in their own adult lives. Their is definitely a correlation.