Yes, in part. He talks in the prophets about Israel growing up as a child before Him, and then when she was grown espousing her to Himself forever. There is beautiful poetic language in Hosea of God’s faithfulness to Israel despite her unfaithfulness.
Jesus gives us salvation and we all receive it.
He guides, protects, shepherds, disciplines, and provides for Israel and then the Church.
Jesus was the Prophet, Priest, and King. He is the Head of the Church, so he must be male to fulfill all of those roles. Only men could be kings and priests.
Men have the God-given task of being the spiritual heads of their families, just like priests and bishops are the spiritual shepherds of their flocks. Jesus was male as the first Priest and as the role-model for all future priests.
We do not call God “Mother.” He loves us more than our earthly mothers and cares tenderly for us, but He is our Father. He gave us Mary for a Mother, and she is also a type of our Holy Mother Church, who cares for us and guides to Heaven.