Can 21st CCLC activities take place during the regular school day?

No.  The statute specifically indicates services are to be provided outside the regular school day or during periods when school is not in session, e.g., before school, after school, evenings, weekends, holidays, or summer.  The program may offer services to students during normal school hours on days when school is not in session, e.g., school holidays or teacher professional development days.