YUP!
And right here we can clearly see what God's intentions were for all mankind when we go back to Gen 3:15! It was never God's intention to save the ungodly seed of the serpent or for the woman's godly seed (ultimately Christ) to die for the serpent's ungodly seed. We can know this because God decreed eternal ENMITY between both seeds! And that enmity between the ungodly extends to all the godly IN Christ, for those in Christ have no fellowship or friendship with the world that is ruled by the serpent (Satan). At the same time, however, we should understand that all God's elect have come into this world with several strikes against them. The elect, in fact differ in no way from the non-elect (see Rom 9:19-21) -- that is to say UNTIL the Potter intervened on their behalf in eternity.
1. Guilty of personal sin
2. Guilty of original sin
3. Came into this world in Adam
4. As a result, Born [spiritually] stillborn, i.e. dead
5. And because of this separation from God spiritually hostile and antagonistic toward him and his Son.
Therefore, the Last Adam, the instrument of God's mediation, came into this world to UNDO all the First Adam's catastrophic damage! This is why Jesus had to lay down his life for the elect [sinners], for without the shedding of blood, there is no remission of sins (Heb 9:22). So, the great paradox here is that by eternal divine decree the elect were always the woman's seed in one sense; yet when they entered this world they entered as the serpent's ungodly seed, i.e. in Adam, for all of us inherited his sin nature. Therefore, in space and time they were actually justified in Christ (as the godly seed they were ordained to be) when they were born again, which occurred when they placed their trust in Christ.