I don’t think it really matters in the grand scheme of things. We know who crushed the head of Satan and we know how He got here. The passage is simply letting us know that there will be someone who will come along and fix things. Whether we interpret it to be Jesus (He) or ‘the seed of the woman’ (she giving rise to He), the result is the same.
It matters in the sense of whether you interpret the passage to mean that “The Woman” will crush the serpent ala Marian devotion and depiction or whether you interpret it as the “seed” of the woman will crush the serpent meaning Jesus as the new Adam.
I will put enmities between thee and the woman,
and thy seed and her seed:
she shall crush thy head,
and thou shalt lie in wait for her heel.
Traditionally, Catholics have interpreted “she” to mean Mary which is why she is often depicted in statue form with a snake under her foot. However, modern translations do not depict that passage the same way. A recent re-translation of the LXX text (the NETS Bible) translates it as “He” rather than “she”. Its also important to note that the statues which do depict Mary with a serpent under her foot do not depict her crushing the head but rather holding it there with the head out.
The Eastern Church to my understanding does not depict Mary in that way but they do make allusions to similar ideas. It is also my understanding that the Orthodox Church views the proper translation as “He” rather than “she” and that they use the LXX rather than MT for their Old Testament translations.
From the Akathist:
*Having shed the light of truth in Egypt, You expelled the darkness of falsehood; and unable to bear Your strength, O Saviour, her idols fell; and they that were set free from them cried to the Theotokos:
Rejoice, Uplifting of men. Rejoice, Downfall of demons.
Rejoice, you who trampled upon the delusion of error. Rejoice, you who censured the deceit of the idols.
Rejoice, Sea which drowned the symbolic Pharaoh. Rejoice, Rock which refreshed those thirsting for life.
Rejoice, Pillar of fire, guiding those in darkness. Rejoice, Protection of the world, more spacious than a cloud.
Rejoice, Nourishment, successor to manna. Rejoice, Minister of holy joy.
Rejoice, Land of promise. Rejoice, you from whom flows milk and honey.
Rejoice, O Unwedded Bride.
*