Sure it does because only sinners need to be saved.
If a person were to be conceived without Original Sin, that person would have been saved from Original Sin. And thus, it would be true to say that she had a Savior.
But, since she was saved from Original Sin by her Savior, she would never have committed a personal sin, and so would not be a “sinner.”
Thus, she would be a sinless person who was saved, by her Savior.
Thus, Mary’s reference to “God my savior” does not imply that she was a sinner.
Sure it does because only sinners need a Lord!