No. Who may be included is decided by relationship and eligibility, not by whose name is on the funding account. An eligible spouse and unmarried children under 21 may accompany or follow you; a 20-year-old is still a child for this purpose. Joint ownership is a source-of-funds question, answered with contribution evidence.
Ownership evidence and derivative eligibility are separate questions
Document the joint account by showing who deposited what and when; that answers provenance. Separately, each family member must be individually admissible, and a child who reaches 21 during a long wait may lose derivative status unless fact-specific age protection applies — no outcome there can be promised in advance. If a delay is driven by archival retrieval, weigh it against a child approaching that age.
Review a child’s age and any applicable protection using the individual dates rather than treating the redemption request as an age freeze. Full-time generally means 35 hours weekly; investor, spouse and children are excluded as qualifying workers, and direct and regional-center methods differ. Rather than assume either the worst or the best, record every child’s exact date of birth at the outset, map it against the expected stages, and take advice specific to those dates.