No, first because the Davidic Covenant is unconditional and is God’s promise to David and Israel that the Messiah would come from the lineage of David and the tribe of Judah and would establish a kingdom that would endure forever. The Davidic Covenant is unconditional because God does not place any conditions of obedience upon its fulfilment. The surety of the promises made rests solely on God’s faithfulness and does not depend at all on David or Israel’s obedience. The Davidic Covenant stands and the ultimate fulfilment will be realised after the millennial reign of Christ Jesus.
Second, the prophecy in Jeremiah about the New Covenant refers, not to the Davidic Covenant but to the Mosaic Covenant which is a conditional covenant made between God and the nation of Israel at Mount Sinai (Exodus 19-24). The blessings and curses that are associated with this conditional covenant are found in detail in Deuteronomy 28. The other covenants found in the Bible are unilateral covenants of promise, in which God binds Himself to do what He promised, regardless of what the recipients of the promises might do. On the other hand the Mosaic Covenant is a bilateral agreement, which specifies the obligations of both parties to the covenant.
Jesus Christ came to fulfil the Law of Moses (Matthew 5:17) and to establish the New Covenant between God and His people. The Old (Mosaic) Covenant was written in stone, but the New Covenant is written on our hearts. Entering the New Covenant is made possible only by faith in Christ, who shed His blood to take away the sins of the world (John 1:29). Luke 22:20 relates how Jesus, at the Last Supper, takes the cup and says, “This cup that is poured out for you is the new covenant in my blood” (ESV).
The Mosaic Law points the way towards the coming of Christ (Galatians 3:24-25). It was replaced by the New Covenant in Christ which fulfils the promises made in Jeremiah 31:31-34, as quoted in Hebrews 8:8-13:
For he finds fault with them when he says: “Behold, the days are coming, declares the Lord, when I will establish a new covenant with the house of Israel and with the house of Judah, not like the covenant that I made with their fathers on the day when I took them by the hand to bring them out of the land of Egypt. For they did not continue in my covenant, and so I showed no concern for them, declares the Lord. For this is the covenant that I will make with the house of Israel after those days, declares the Lord: I will put my laws into their minds, and write them on their hearts, and I will be their God, and they shall be my people. And they shall not teach, each one his neighbor and each one his brother, saying, ‘Know the Lord,’ for they shall all know me, from the least of them to the greatest. For I will be merciful toward their iniquities, and I will remember their sins no more.” In speaking of a new covenant, he makes the first one obsolete. And what is becoming obsolete and growing old is ready to vanish away.
“Therefore he [Christ] is the mediator of a new covenant, so that those who are called may receive the promised eternal inheritance, since a death has occurred that redeems them from the transgressions committed under the first covenant” (Hebrews 9:15).
The New Covenant blessings are open to the House of Israel and the House of Judah. After the resurrection of Christ, Gentiles were also brought into the New Covenant (Ephesians 2:11–22).
EDIT: Where “the house of Israel and the house of Judah” are mentioned in Jeremiah 31:27 and 31, The Companion Bible draws attention to the union of the two houses. “Israel is always named first, for this was the name of the whole nation, which Judah was not.” The house of Israel was composed of two tribes, and the house of Judah was composed of ten tribes.
Why is the house of Judah mentioned here in Jeremiah, along with the house of Israel? Judah was the fourth son born to Jacob (Genesis 29:30) but he inherited the rule after his three older brothers disqualified themselves by gross misconduct. Simeon and Levi broke their father’s covenant and slaughtered an entire people (Genesis 34). Reuben disgraced himself with Jacob’s concubine (1 Chronicles 5:1-2). Jacob prophesied that
the sceptre shall not depart from Judah, nor a lawgiver from between his feet, until Shiloh come; and unto him shall the gathering of the people be (Genesis 49:9-10).
Quoting Isaiah 11:1-2, with regard to the Gentiles, Romans 15:12 refers to the father of David:
The Root of Jesse will spring up, one who will arise to rule over the nations; the Gentiles will hope in him.
The significance and importance attached to Judah is borne out in Revelation 5:5 which refers to Jesus as “the Lion of the tribe of Judah, the Root of David”.
P.S. My understanding is that the old covenant refers to the Mosaic Law inaugurated at Sinai (Exodus 24:3-8) which is conditional and not to the Davidic covenant which is unconditional and does not equate to law.