No, because you speak only of the mortal body, and cut off the rest of the story:
O death, where is thy sting? O grave, where is thy victory?
The sting of death is sin; and the strength of sin is the law.
But thanks be to God, which giveth us the victory through our Lord Jesus Christ.
Paul is speaking of the death of the soul, which is the sting of being separated from the life of Christ. The death of the body is not just a sting, but an end in the grave.
It's the soul and spirit of man that obeys the law of Christ with the body: no natural flesh and blood on earth, has a spirit in it's own tissues to obey or disobey anything.
The soul is resurrected unto life and righteousness now, or remains dead in sins and trespasses beyond the grave.
True. Naturally so. All natural men can see and know this.
It's only the carnal minded, that rejects a resurrection of the mortal flesh into immortal spiritual bodies.
There is no birth with sin nature, neither in the soul nor the flesh, but the result of flesh being made mortal by Christ, is the same: death of the mortal body, not by sinning, but by the nature of all flesh on earth, which is mortality.
And so, this is where you insert your mortal soul natural theology.
This is how you teach the soul dying only with the body, and not spiritually before by sinning against God: you believe the mortal body is the body of the soul.
You teach the soul is flesh and blood only: man is a flesh and blood soul.
By your theology, you are only calling the body a soul, instead of just calling the body what it is: a body. Which is what all men do, whether natural or spiritual. You're in between, by calling the body a soul, which is meaningless, since they are the same thing to you. Soul is just another name for body.
You also combine two errors to make a greater error: first that the soul is flesh and blood only, and that all souls are born sinful flesh and blood, by the sinning of Adam.
Hence, your naturalism combined with a sin nature, makes souls bodies born mortal to return to the dust by sinning.
This is why you must reject Jesus Christ as God coming in the flesh, because his flesh and blood soul would have to be immortal, so that he would still be on the earth today, in His born flesh and blood.
However, since you also believe all flesh and blood souls of men only die by sinning, then you cannot believe the man Jesus did not sin at all, because He died like all men in the flesh.
You reject the spiritual truth of Scripture, that souls are not flesh and blood alone, but we are spiritually created living beings temporarily in mortal bodies.
Therefore, when the soul sins, it's the body doing the sinning, so that the soul only dies with the body.
You therefore also reject this Scripture:
Even when we were dead in sins, hath quickened us together with Christ, (by grace ye are saved).
Your natural theology would have to say the body of the soul was dead once on earth, while yet walking around. Like some walking dead zombie flick.