If Jesus was God from the moment of his conception, and Mary gave birth to God then yes, she is the mother of God. But she didn’t contribute his God nature, only his man nature. As long as she is the birth mother to a person who was fully God and fully Man at the same time, she is his mother, no matter what part she contributed.
Saying she’s the mother of only the man side of Jesus is saying that only the man part of Jesus was there at his birth. Did you mean that?