No, the wicked are separated from God. We find what happens if we read what it says in Revelation at the end of the thousand years of the Millennium..It's hard to call the ultimate state of the wicked "life" at all, in any meaningful sense. The damned exist, but to say they have life, let alone eternal life, fundamentally misunderstands what eternal life means in any meaningful biblical sense.
The wicked experience a state of second death--conscious, aware, but alive? hardly. They exist in a state of deliberate rejection of life.
Revelation 20:7-9
7 And when the thousand years are expired, Satan shall be loosed out of his prison,
8 And shall go out to deceive the nations which are in the four quarters of the earth, Gog, and Magog, to gather them together to battle: the number of whom is as the sand of the sea.
9 And they went up on the breadth of the earth, and compassed the camp of the saints about, and the beloved city: and fire came down from God out of heaven, and devoured them.
The Wicked are "devoured" by the fire from God after the thousand year reign of Christ with His saints in heaven, all those who have not received the mark of the beast or its image as we see.
Revelation 20:4
And I saw thrones, and they sat upon them, and judgment was given unto them: and I saw the souls of them that were beheaded for the witness of Jesus, and for the word of God, and which had not worshipped the beast, neither his image, neither had received his mark upon their foreheads, or in their hands; and they lived and reigned with Christ a thousand years.
Now the reason the saints are in reigning in heaven is they will also be involved in an important phase of His governing—judgment. Judging the unrighteous who have died, the devil, and the fallen angels. This is what Paul meant when he said that the saints will judge the world and even angels..
1 Corinthians 6:2-3
2 Do ye not know that the saints shall judge the world? and if the world shall be judged by you, are ye unworthy to judge the smallest matters?
3 Know ye not that we shall judge angels? how much more things that pertain to this life?
During the thousand years of the Millennium, the saints reign in heaven between the first and second resurrections, the first being of the saints at the Second Coming.
Revelation 20:5-6
5 But the rest of the dead lived not again until the thousand years were finished. This is the first resurrection.
6 Blessed and holy is he that hath part in the first resurrection: on such the second death hath no power, but they shall be priests of God and of Christ, and shall reign with him a thousand years.
We see the second one of the wicked at the end of the thousand years, "rest of the dead lived not again until the thousand years were finished."
At the time of the thousand years of the Millennium, the wicked dead will be judged; the earth will be utterly desolate, without living human inhabitants, but still inhabited by Satan and his angels. We see Jeramiah describing what it looks like..
Jeremiah 4:23-26
23 I beheld the earth, and, lo, it was without form, and void; and the heavens, and they had no light.
24 I beheld the mountains, and, lo, they trembled, and all the hills moved lightly.
25 I beheld, and, lo, there was no man, and all the birds of the heavens were fled.
26 I beheld, and, lo, the fruitful place was a wilderness, and all the cities thereof were broken down at the presence of the Lord, and by his fierce anger.
And the clearing of the earth in Zephaniah..
Zephaniah 1:18
Neither their silver nor their gold shall be able to deliver them in the day of the Lord's wrath; but the whole land shall be devoured by the fire of his jealousy: for he shall make even a speedy riddance of all them that dwell in the land.
This is how Satan is bound as there is no one to temp, much like the earth before Adam and Eve " it was without form, and void", a bottomless pit.
Revelation 20:2-3
2 And he laid hold on the dragon, that old serpent, which is the Devil, and Satan, and bound him a thousand years,
3 And cast him into the bottomless pit, and shut him up, and set a seal upon him, that he should deceive the nations no more, till the thousand years should be fulfilled: and after that he must be loosed a little season.
At its close, Christ with His saints and the Holy City will descend from heaven to earth. The unrighteous dead will then be resurrected, and with Satan and his angels will surround the city; but fire from God will consume them and cleanse the earth. This is what is meant by "destroy both soul and body in hell", the person can die the death of all men, but the Second Death is the separation from God.
The Great White Throne judgement is the courtroom scene after the second resurrection of the dead, all the wicked in all aspects, in the graves or the oceans, so that the whole universe may see that God is just, and the wicked are separated from God at the Second Death.
11 And I saw a great white throne, and him that sat on it, from whose face the earth and the heaven fled away; and there was found no place for them.
12 And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works.
13 And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works.
14 And death and hell were cast into the lake of fire. This is the second death.
The universe will thus be freed of sin and sinners forever.
Jude 1:7 Even as Sodom and Gomorrha, and the cities about them in like manner, giving themselves over to fornication, and going after strange flesh, are set forth for an example, suffering the vengeance of eternal fire.
Their punishment like the example given on Sodom and Gomorrha, a eternal separation from God which will not be reversed or allowed to come back, thus its results are "eternal".
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