No. Hegseth quoted a prayer used by the Search and Rescue team that recovered the crew of the downed F15E. The CSAR team, call sign Sandy1, have clearly adapted the Samuel L Jackson speech to their own ends, but Hegseth was merely quoting them, not the film;
"They call it CSAR 25:17, which I think is meant to reflect Ezekiel 25:17. It reads — and pray with me please — ‘the path of the downed aviator is beset on all sides by the inequities of the selfish and the tyranny of evil men. Blessed is he who in the name of camaraderie and duty shepherds the lost through the valley of darkness, for he is truly his brother’s keeper and the finder of lost children. And I will strike down upon thee with great vengeance and furious anger those who attempt to capture and destroy my brother, and you will know my call sign is Sandy 1 when I lay my vengeance upon thee. Amen.”