I agree with all that. But not with what you assume to be implied.
Let me put it like this: What do you think makes it possible for the enemies of God to place their trust and love in him ("accept that free gift")?
What makes it possible is the same reality that believers who walk in the Spirit's control can know. Carnal believers can not know...
Your depravity resides in the body. Not in your soul. If the Spirit controls your flesh (by grace) your soul can be made free to think for itself without the tyranny of the flesh dominating over your real self - your soul.
For we know that the law is spiritual, but I am carnal, sold under sin. For
what I am doing, I do not understand. For what I will to do, that I do not
practice; but what I hate, that I do. If, then, I do what I will not to do, I
agree with the law that it is good. But now, it is no longer I who do it,
but sin that dwells in me. For I know that in me (that is, in my flesh)
nothing good dwells; for to will is present with me, but how to perform
what is good I do not find. For the good that I will to do, I do not do; but
the evil I will not to do, that I practice. Now if I do what I will not to do, it is
no longer I who do it, but sin that dwells in me." Rom 7:14-20
Its in your flesh that depravity dwells. Not your soul. The soul is simply a helpless victim of the flesh. God's grace power enabling makes the maturing believer able l to think with his soul free of the sin nature's dominance!
Those who are maturing in Christ will understand the meaning of the following truth!The depravity will not be allowed to reign over one's soul!
I say then: Walk in the Spirit, and you shall not fulfill the lust of the flesh" Gal 5:16
Now, in drawing all men to salvation? God sovereignly administers grace power to control the flesh of the one being drawn. Grace makes it so his flesh will not hinder the soul, so that soul can make a real choice for, or against God.
Romans 1:18-22 shows how men, whom God has made it clear to, were still free to reject Him.
But, there is one difference when we reject while grace is present. When one rejects God while His grace is making the soul free to choose? The sin nature at that point was out of the picture. So, one can not say the rejection was sin. This is the difference between what constitutes 'sin,' and what constitutes 'evil.'
For it was by evil that Satan rejected the Lord, while yet in his unfallen state!
You were perfect in your ways from the day you were created, till iniquity
was found in you." Ezek 28:15
God did not create Satan with a sin nature! Originally, evil was Satan's downfall... which then led to sin.
grace and peace! .........