No. Non-Christians live in the New Earth under the New Heavens but they are outside the City of the New Jerusalem, which represents the New Testament,
LINK. They are under the rule of the new order of things even though they remain outside the blessings of obedience to it. This question, like so many others, can be cleared up easily by simply looking at the actual verses related to the question:
Revelation 21:1-8
Then I saw a new heaven and a new earth, for the first heaven and the first earth had passed away, and there was no longer any sea. 2 I saw the Holy City, the new Jerusalem, coming down out of heaven from God, prepared as a bride beautifully dressed for her husband. 3 And I heard a loud voice from the throne saying, "Now the dwelling of God is with men, and he will live with them. They will be his people, and God himself will be with them and be their God. 4 He will wipe every tear from their eyes. There will be no more death or mourning or crying or pain, for the old order of things has passed away." 5 He who was seated on the throne said, "I am making everything new!" Then he said, "Write this down, for these words are trustworthy and true."6 He said to me: "It is done. I am the Alpha and the Omega, the Beginning and the End. To him who is thirsty I will give to drink without cost from the spring of the water of life. 7 He who overcomes will inherit all this, and I will be his God and he will be my son. 8 But the cowardly, the unbelieving, the vile, the murderers, the sexually immoral, those who practice magic arts, the idolaters and all liars — their place will be in the fiery lake of burning sulfur. This is the second death."
NIV
v1 Then I saw – John is introducing another mini-vision that describes with visual-poetry direct consequences of Babylon’s Fall, reasons for the Heavens’ rejoicing over Babylon.
v4b - “…for the old order of things has passed away." – John explains what the imagery of the passing of the first heaven&earth represent. The change from the Old to the New had finally been made visible with the removal of the Old Jerusalem and the establishing of the Church as the ONLY Temple of God among men. The old order of commandments and judgments has passed away but a new order of commandments and judgments have come to rule in its place. The Old Testament order has passed and the New Testament order has been established. This affects both believers and unbelievers by ruling over them all according to the same New Testament Law of Christ; blessings for those obedient to the New Testement order, judgment for those disobedient to the New Testament order.
v7 – explains that the blessings that have been described are strictly reserved for “he who overcomes.” This same John is the one who penned,
1 John 5:4-5
4 For whatsoever is born of God overcometh the world: and this is the victory that overcometh the world, even our faith.
5 Who is he that overcometh the world, but he that believeth that Jesus is the Son of God?
v8 – Though verse 8 here seems to say that “the cowardly, etc.” will find their place elsewhere, namely, in the Second Death, John had just made clear in Rev 20:12-15 that unbelievers are placed there after their individual Judgment that follows their individual death, Hebrews 9:27. And the vision reinforces this by stating later on,
Revelation 22:14-15 Blessed are those who do His commandments, that they may have the right to the tree of life, and may enter through the gates into the city. 15 But outside are dogs and sorcerers and sexually immoral and murderers and idolaters, and whoever loves and practices a lie.
NKJV
