Yes — for Israel in Egypt, redemption means God buying back His covenant people over whom He had lost control.
Because the brothers' sin sent Joseph to Egypt and the whole family followed, Israel was outside the land of promise and in bondage to the pagan Egyptians. In that practical sense God had lost control of Israel and had to buy them back. That is why Exodus is called the book of redemption; God's act of redemption began with the blood of the Passover lamb.
Exodus 6:6 — This is God's own declaration that He will redeem the children of Israel out of Egypt — the central verse behind the question.
Scripture directly presents redemption as God's own promise to Israel in Egypt. In Exodus 6:6 the LORD tells Moses: "Wherefore say unto the children of Israel, I am the LORD, and I will bring you out from under the burdens of the Egyptians, and I will rid you out of their bondage, and I will redeem you with a stretched out arm, and with great judgments:" In the verses that follow, God continues: "And I will take you to me for a people, and I will be to you a God: and ye shall know that I am the LORD your God, which bringeth you out from under the burdens of the Egyptians." And He promises, "And I will bring you in unto the land, concerning the which I did swear to give it to Abraham, to Isaac, and to Jacob; and I will give it you for an heritage: I am the LORD." These verses show that redemption in this context is God buying His people out of Egypt and restoring them to the land He promised.
Les Feldick defines redemption as buying back something over which control has been lost. He uses the everyday illustration of a paid-for home that is mortgaged: to get it back, you have to redeem it. He then applies that same definition to Israel in Egypt. God had told Abraham, Isaac, and Jacob to remain in the land of promise, but when Joseph's brothers sold him into slavery and the family later went down to Egypt, Israel ended up outside that land and under the influence of Egyptian idolatry. In a practical sense, God 'lost control' of His covenant people, so He had to buy them back. Les teaches that this is the whole story of the book of Exodus — it is the book of redemption. God bought His covenant people out of the slave market of Egypt. The process began with the blood of the Passover lamb on the doorposts, and continued as God led Israel out through Moses to the Red Sea. In Exodus 6, God announced, "I will... redeem you." Les also points out that the same idea of redemption appears in our own salvation — the buying back that is in Christ Jesus.
Les explains that the sin of Joseph's brothers is what started it: they sold Joseph into Egypt, and eventually all twelve sons went down into Egypt. At that point Israel was outside the land of promise and under the influence of Egyptian idolatry and bondage. He says God lost control of His covenant people and had to redeem them.
Les calls Exodus the book of redemption because God bought His covenant people out of the slave market of Egypt. He likens it to redeeming a mortgaged home: when you lose control of something, you buy that control back. For Israel, this began with the Passover lamb's blood on the doorposts and continued with God leading them out through Moses to the Red Sea.
In Exodus 6, God says He will bring Israel out from under the burdens of the Egyptians, rid them of their bondage, and redeem them with a stretched out arm. He then promises to take them as His people and bring them into the land He swore to Abraham, Isaac, and Jacob. This shows that redemption is God's own saving action toward Israel.
Les points out that God redeeming Israel out of Egypt is the same concept as our redemption through Christ. Just as God had to pay the price to buy Israel back, believers are justified through the redemption or buying back that is in Christ Jesus. However, he keeps the two distinct: Israel's redemption was through the blood of the Passover lamb, and ours is through Christ.
God's Command to Stay in the Land
Les shows that God had told Abraham, Isaac, and Jacob not to leave the land of promise, so Israel's removal to Egypt set the stage for God having to redeem them.
Israel Mortgaged to Egypt
Israel lost fellowship with Abraham's God and became mortgaged to the pagan Egyptians, so God had to buy them back; redemption began with the blood of the Passover lamb on the doorposts.
Sin of the Brothers Caused God to Lose Control
The brothers' sale of Joseph set the ball rolling: God lost control of His covenant people in Egypt and had to redeem them.
Exodus as the Book of Redemption
Exodus is the book of redemption because God bought His covenant people out of the slave market of Egypt; Les defines redemption as buying back something you have lost control over.
God's Promise to Redeem in Exodus 6
God speaks of redeeming the children of Israel out of Egypt, paying the price to buy them back — just as He later did for believers in the age of grace.
The Nation of Israel Lost and Bought Back
Israel were God's covenant people until the brothers' sin sent Joseph to Egypt; God lost His chosen people and bought them back through the blood of the Passover lamb.
Redemption from the Beginning
Les connects the whole Old Testament concept of redemption back to Adam and Eve — once God lost control to Satan, redemption meant buying them back — and then applies the same pattern to Israel.
God's Own Words: 'I Will Redeem You'
God told Moses to say to Israel, "I will... redeem you," buying them back and setting them free from the bondage of Egypt.
Exodus 6:6: Wherefore say unto the children of Israel, I am the LORD, and I will bring you out from under the burdens of the Egyptians, and I will rid you out of their bondage, and I will redeem you with a stretched out arm, and with great judgments:
This is God's direct promise to redeem the children of Israel out of Egypt, showing that redemption means being bought out of bondage.
Exodus 6:7: And I will take you to me for a people, and I will be to you a God: and ye shall know that I am the LORD your God, which bringeth you out from under the burdens of the Egyptians.
God states the purpose of redemption: Israel will be His people and know Him as the LORD.
Exodus 6:8: And I will bring you in unto the land, concerning the which I did swear to give it to Abraham, to Isaac, and to Jacob; and I will give it you for an heritage: I am the LORD.
God ties redemption to bringing Israel back into the land promised to Abraham, Isaac, and Jacob.
Redemption means buying back something over which control has been lost. Les illustrates this with a mortgaged home: when you mortgage a paid-off house, you must redeem it to regain full ownership. In the Bible, God redeems His people by paying the price to bring them back to Himself.
Because God bought His covenant people out of the slave market of Egypt. They had lost fellowship and were in bondage, so God had to buy them back, beginning with the Passover blood and leading them to the Red Sea.
In a practical sense, yes. Les says the brothers' sin caused God to lose control of His covenant people when they were in Egypt. Because they were under Egyptian idolatry and bondage, God had to redeem them — buy them back — even though He still had His covenants uppermost.
Watch the Teaching: Joseph as a Type of Christ: The Hidden Prophecy in Genesis 37-46