"The first intimation of such a hope was given to Adam and Eve in the sentence pronounced upon the serpent in Eden when the Lord declared to Satan in their hearing, “I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise His heel.” Genesis 3:15 . PK 681.2"
"And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel."
The EGW passage directly quotes Genesis 3:15 and uses it as the first intimation of hope for a deliverer.
"As the guilty pair listened to these words, they were inspired with hope; for in the prophecy concerning the breaking of Satan's power they discerned a promise of deliverance from the ruin wrought through transgression. Though they must suffer from the power of their adversary because they had fallen under his seductive influence and had chosen to disobey the plain command of Jehovah, yet they need not yield to utter despair. The Son of God was offering to atone with His own lifeblood for their transgression. To them was to be granted a period of probation, during which, through faith in the power of Christ to save, they might become once more the children of God. PK 681.3"
"But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us."
Both passages deal with the hope of redemption offered through Christ after sin entered the world. Romans 5:8 speaks of Christ's death for sinners, while the EGW passage speaks of the promise of deliverance through Christ's sacrifice after the fall. The connection is thematic, but not a direct allusion.