No, Nestorianism does not permit same-sex marriage.

Nestorianism is the doctrine that Jesus exists as two persons, the man Jesus and the divine Son of God, or Logos, rather than as a unified person.

The Nestorianism heresy maintained that Christ had two persons one human and one divine, so it condemned the use of the word Theotokos, greek for bearer or mother of God. If Jesus was two persons, then Mary gave birth only to the human person, not the divine. So, Nestorianism challenged the Churches use of the title Mother of God. A Ecumenical Council was convened in Ephesus in A.D. 431 to establish that Jesus is one person, with two natures one human and one divine, and Mary gave birth to him so she is the Mother of God.

St. Cyril of Alexandria was known for his role in the Christological controversies of the 5th century, particularly his defense of the title "Theotokos" (Mother of God) for the Virgin Mary and his writings on the unity of Christ's divine and human natures. He also played a significant role in the Council of Ephesus in 431, which affirmed Mary as Theotokos and condemned Nestorianism.