No.
First, the "book of the covenant" mentioned in verse 7 is a reference to the covenant made with Abraham (as well as Isaac and Jacob, the other patriarchs). Second, the "blood of the covenant" is Christ's blood, not that of animals. The sacrifices and their blood was simply a foreshadowing, and a shadow of what was to come.
Hebrews 10:1-4
For the Law, since it has only a shadow of the good things to come and not the very form of things, can never, by the same sacrifices which they offer continually year by year, make perfect those who draw near. Otherwise, would they not have ceased to be offered, because the worshipers, having once been cleansed, would no longer have had consciousness of sins? But in those sacrifices there is a reminder of sins year by year. For it is impossible for the blood of bulls and goats to take away sins.
The Law was a shadow, not the real thing. Furthermore, the word "atone" is an English word. The Hebrew word used in Exodus is "kaphar" and it means to cover over. The blood of animals covered over the sins, but it did not make them go away. Nor did it pay the debt incurred.
The covenant was made with Abraham and Jesus (Abraham's seed). All the other mentions of "covenant" throughout the OT are tied to the promises made to Abraham and Jesus.
Deuteronomy 7:7-8
The LORD did not set His love on you nor choose you because you were more in number than any of the peoples, for you were the fewest of all peoples, but because the LORD loved you and kept the oath which He swore to your forefathers, the LORD brought you out by a mighty hand and redeemed you from the house of slavery, from the hand of Pharaoh king of Egypt.
Not all Israel is Israel. When God speaks of "the sons of Israel" He is ALWAYS speaking about the Israel that is Israel, not the Israel that is not Israel. In Exodus 24 the nation-state of Israel did not yet exist. Israel was the name God gave to Jacob because he prevailed with God over himself...... by faith and NOT by the works of the Law. God did not choose those to whom He was speaking in Exodus 24 because they were big, or strong, or pretty, or smelled good. There was nothing specifically about them that prompted God in any way to choose them. God chose them to keep the promise He had made to their forefathers centuries before anyone in Exodus 24 was even born.
Romans 9:6-16
But it is not as though the word of God has failed. For not all who are descended from Israel belong to Israel, and not all are children of Abraham because they are his offspring, but “Through Isaac shall your offspring be named.” This means that it is not the children of the flesh who are the children of God, but the children of the promise are counted as offspring. For this is what the promise said: “About this time next year I will return, and Sarah shall have a son.” And not only so, but also when Rebekah had conceived children by one man, our forefather Isaac, though they were not yet born and had done nothing either good or bad—in order that God’s purpose of election might continue, not because of works but because of him who calls— she was told, “The older will serve the younger.” As it is written, “Jacob I loved, but Esau I hated.” What shall we say then? Is there injustice on God’s part? By no means! For he says to Moses, “I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion.” So then it depends not on human will or exertion, but on God, who has mercy.
The Hebrews of Exodus 24 did not earn the privilege of a covenant relationship with God any more than the Gentiles have. God has mercy on who He wants to have mercy and it does NOT depend on how a man wills or works. It depends solely on the will of and purpose of God. The will of God is that the older should serve the younger. Old covenant serves new covenant, not the other way around. Old converts serve new converts. In this case that mean those men and women of faith are made complete in the Church, not the other way around.
Hebrews 11:39-40
And all these, having gained approval through their faith, did not receive what was promised, because God had provided something better for us, so that apart from us they would not be made perfect.
Those sons of Israel were made perfect in Christ and his body. They were made perfect in the seed promised Abraham that is Christ resurrected.