The answer is Yes. Jesus, the Son of God, existed before he was given a physical body and born by Mary. Just as he exists after his earthly body died.
Jesus is the Savior, not Mary.
what you posted is perfect from the Catholic Faith teaching:
God the Son has always existed, He was without beginning or end and in the fullness of time He became Man, so He is fully God and fully man.
Jesus is the only Savior of the world, He alone is the mediator between God and men, His Sacrificial death on the cross reconciles sinners to God. Mary is a created human being, who became the Mother of God.
Actually, the second person of the Trinity is eternal, Jesus, the Word Incarnate did not exist until conceived in the womb of Mary through the power of the Holy Spirit.