Yes, TD dependants may study in the United States, and unmarried children under 21 qualify. They cannot work, and their status ends when they turn 21 or marry, whichever comes first, so a child close to that age needs a separate plan.
Study is permitted; work and ageing out are the limits
TD status covers a spouse and unmarried children under 21, and official guidance confirms that TD holders may enrol in school without changing status. For a Lac-Beauport household with children in secondary school this usually works cleanly. The difficulties are at the edges.
A 19-year-old who wants a part-time job while studying cannot take one on TD. A child who turns 21 during the principal's assignment loses TD status on that birthday, regardless of where they are in a degree, and would need to qualify for a student classification or another category in their own right. A spouse who intends to work cannot rely on TD either; unlike L-2 and E-2 spouses, TD spouses are not employment-authorized, and remote work for a Québec employer while living in the United States is still work.
Record each child's birth date and the intended assignment period side by side before accepting a multi-year offer.