Yes, I believe it makes (shows) a separation from all mankind and the elect.
And I will put enmity Between you and the woman, And between your seed and her Seed; . . . . The seed of the woman seed is opposed to the seed of the serpent. Now, it couldn't mean just Jesus, if it did, then how would Satan's seed make sense?
The only seed Satan has is,
Ye are of your father the devil, and the lusts of your father ye will do. He was a murderer from the beginning, and abode not in the truth, because there is no truth in him. When he speaketh a lie, he speaketh of his own: for he is a liar, and the father of it. John 8:44.
He that committeth sin is of the devil; for the devil sinneth from the beginning. For this purpose the Son of God was manifested, that he might destroy the works of the devil. 1 John 3:8
The field is the world; the good seed are the children of the kingdom; but the tares are the children of the wicked one; Matt 13:38.
Which, as you stated above, the church will war with the seed of the serpent.