No. If a Cuban national has taken up residence in the United States and has applied to become a lawful permanent resident alien of the United States and has an adjustment of status application pending, then the Cuban national is considered unblocked and does not need to apply to OFAC to be treated as an unblocked national, provided that he or she is not a prohibited official of the Government of Cuba or a prohibited member of the Cuban Communist party. See 31 CFR § 515.505(a)(1).
A Part of Treasury's Office of Terrorism and
Financial Intelligence
Financial Intelligence