No. Accompanying family is limited to a spouse and unmarried children under twenty-one, and each of those adds both a further processing fee and a further gift of one million United States dollars. A child of twenty-two has aged beyond the derivative definition and needs a route of their own.
The birthday, not the tuition bill, decides it
Aloysius has been budgeting for a household of four and can include three. His nineteen-year-old son may be included while he remains unmarried and under twenty-one, and that inclusion is not free, since each accompanying person carries a fee and an additional gift of one million dollars. His daughter cannot be included at twenty-two, however dependent she remains in practice.
Her options are the ones any adult foreign national has and should be examined on their own merits: study in her own right, an employment-based category if an American employer will petition, or a family-based petition from a parent once that parent holds permanent residence, which carries its own waiting period. The general rule under every route on this site holds here too. Each person's age, marital status and intended activity determine their own route, and no adult is carried along on a parent's application.