Indeed He would as he recited Psalm 21 (22) upon the Cross. The Gospels only record the the first verse but it is quite obvious that Our Lord would have recited it in it's entirety.  
It basically records the ignominious treatment of the Son of God during His Passion to His victory over death by the end of it. Most people, these days are led to believe that He was admonishing the Father: no such thing.
Verse 20 reverses the Psalm of the suffering servant to his vindication: "But thou, O Lord, remove not thy help to a distance from me; look towards my defence et reliqua."
Finally, "And to him my soul shall live: and my seed shall serve him.
There shall be declared to the Lord a generation to come: and the heavens shall shew forth his justice to a people that shall be born, which the Lord hath made."
This is certainly no song of submission.