No. Tuition or an enrollment deposit is a separate private obligation, not the published gift to the United States.
Keep two budgets with different conditions
Each eligible joining relative currently adds US$1 million and US$15,000 processing. Review the school’s actual refund and deferral terms independently; this page does not promise that educational payments are recoverable if immigration timing changes. Two budgets with different rules, and the difference that matters is what happens if the plan changes.
Tuition and enrollment deposits are governed by the school’s own refund and deferral terms, which the family can read and, occasionally, negotiate. The published government amounts are governed by nothing the family can negotiate. Ask the school, before the deposit is paid, what is returned if the family withdraws at each of three points — before the term begins, after it begins, and after the first invoice falls due — and get the answer in writing.
A school that will not put its refund terms in writing has told you something useful about the order in which to pay. Decide in advance which budget absorbs a change of plan, because the two behave differently under pressure: the school’s terms may permit a deferral that preserves the deposit, while a nonrefundable processing payment stays spent whatever the family decides next. Write that asymmetry into the plan before either amount is paid, and keep the two payment dates apart so that one does not force the other.