Sunday School is church. Maybe the classrooms are located next door to the auditorium (or in the basement), but Sunday School isn't a separate entity or appendage.
For one thing, the Christian Science Sunday School has the same pastor that the church congregation has—the Bible and Science and Health by Mrs. Eddy. The pastor is just as active in the Sunday School as it is in the church auditorium.
Isn't the church really composed of all its activities, each working with the others to fulfill the purpose for which the whole Church of Christ, Scientist, was founded? When the Church was instituted, it was on Mrs. Eddy's motion "To organize a church designed to commemorate the word and works of our Master, which should reinstate primitive Christianity and its lost element of healing."
Manual of The Mother Church, p. 17 .And the Sunday School is designed to do just that.