Not really. In the Old Testament, sinners were put to death in order for them to be reconciled to God, as "payment" for their offense. As Hebrews 9:22 says "Without the shedding of blood, there is no remission."
There were some sins, in which the person was exiled, "cut off from among his people" which was thought to be worse than death, because it represented a "separation" from God as well as his/her people. Those who accept Christ are not in exile, in life, or death, and have no need to fear the penalty of death, for sin.
sinners were certainly, at times, put to death fro their sins.... but this death was not effacacious in any way as an atonement for their sins.. the only way... the ONLY way someone can be saved, is if Christ propitiated and expiated their sins before a just and holy God.... and the ONLY way they can be saved is by faith in the Son.....
(Romans 3:22-25) the righteousness of God through faith in Jesus Christ for all who believe. For there is no distinction: for all have sinned and fall short of the glory of God, and are justified by his grace as a gift, through the redemption that is in Christ Jesus, whom God put forward as a propitiation by his blood, to be received by faith. This was to show God's righteousness, because in his divine forbearance he had passed over former sins."
(Hebrews 2:17-18) Therefore he had to be made like his brothers in every respect, so that he might become a merciful and faithful high priest in the service of God, to make propitiation for the sins of the people. For because he himself has suffered when tempted, he is able to help those who are being tempted.
(1 John 2:1-2) My little children, I am writing these things to you so that you may not sin. But if anyone does sin, we have an advocate with the Father, Jesus Christ the righteous. He is the propitiation for our sins, and not for ours only but also for the sins of the whole world.
(1 John 4:10) In this is love, not that we have loved God but that he loved us and sent his Son to be the propitiation for our sins.
the death of a sinner may have been the penalty for a given sin, but that death did not expiate or propitiate God's wrath towards their sin.... because their death would have been the death of an unclean lamb.... only Christ was the perfect spotless lamb,
(John 1:29) The next day he saw Jesus coming toward him, and said, "Behold, the Lamb of God, who takes away the sin of the world!
(1 Peter 1:17-19) And if you call on him as Father who judges impartially according to each one's deeds, conduct yourselves with fear throughout the time of your exile, knowing that you were ransomed from the futile ways inherited from your forefathers, not with perishable things such as silver or gold, but with the precious blood of Christ, like that of a lamb without blemish or spot.
only His perfect life, death, atonement and intercession can save someone... a person cannot be saved by their own name, by their own death because they are not a worthy sacrifice... only by Jesus'...
(Acts 4:12) And there is salvation in no one else, for there is no other name under heaven given among men by which we must be saved."
all sacrifices.... all the shedding of blood prior to the coming of Christ, never atoned for their sins.... EVER....
(Hebrews 10:3-6) But in these sacrifices there is a reminder of sin every year. For it is
impossible for the blood of bulls and goats to take away sins. Consequently, when Christ came into the world, he said, "Sacrifices and offerings you have not desired, but a body have you prepared for me;
in burnt offerings and sin offerings you have taken no pleasure.
(Hebrews 9:11-12) But when Christ appeared as a high priest of the good things that have come, then through the greater and more perfect tent (not made with hands, that is, not of this creation) he entered once for all into the holy places,
not by means of the blood of goats and calves but by means of
his own blood, thus
securing an eternal redemption.
.....these sacrifices were all just imperfect shadows of what was to come in Christ....
(Hebrews 8:4-7) Now if he were on earth, he would not be a priest at all, since there are priests who offer gifts according to the law. They serve a copy and shadow of the heavenly things. For when Moses was about to erect the tent, he was instructed by God, saying, "See that you make everything according to the pattern that was shown you on the mountain." But as it is, Christ has obtained a ministry that is as much more excellent than the old as the covenant he mediates is better, since it is enacted on better promises. For if that first covenant had been faultless, there would have been no occasion to look for a second."
blessings