Yes. Unmarried children under 21 hold derivative status and may attend school in the United States without a separate student route. That derivative status ends at 21, and a young adult who intends to continue studying after that point needs an independent basis such as enrolment at a school certified by the Student and Exchange Visitor Program.
Study is permitted now; the twenty-first birthday is the planning problem
Hypothetical example: Anouk would be assigned to the American affiliate for two years, and her household includes a teenager approaching adulthood. For school-age children the position is simple and is often the least stressful part of a move: derivative status permits enrolment, and no separate application is needed to attend school. The complication arrives with older teenagers on a multi-year assignment.
Derivative status is available only while a child is unmarried and under 21, so a seventeen-year-old accompanying Anouk on a two-year assignment that is later extended may reach that birthday in the middle of a degree. The transition is not automatic. It requires an independent route, most commonly acceptance and enrolment at a certified institution with the accompanying record issued by that school, and it should be prepared a year ahead rather than in the final weeks.
Costs change as well, since dependants and independent students are treated differently for tuition purposes by many institutions. Map every child's birthday against the assignment before the family commits.