No, it will give mankind a first chance for redemption. Presently, God is not trying to save the entire world! If He were, He would be failing in His task… Think about it.
What is God doing now? He is calling out a small group of footstep followers of Christ. They are called by various names: the bride of Christ, the church class, the little flock, the saints. These precious saints have accepted Christ as their Savior, and are denying themselves, taking up their crosses, and following Him. (Matthew 16:24) Through obedience to their Savior, they are growing the fruits of the spirit and are being transformed into His character likeness. (Romans 12:2) For their faithfulness, they are promised a heavenly resurrection and will reign with Christ in heaven. (Revelation 20:4)
Jesus, Himself, told us He was not trying to convert the world right now. Matthew 13:10-15, “The disciples …asked, Why do you speak to the people in parables? He (Jesus) replied, The knowledge of the secrets of the kingdom of heaven has been given to you, but not to them…For this people’s heart has become calloused; they hardly hear with their ears, and they have closed their eyes…”
Presently, God has permitted Satan to blind mankind. “The god of this age has blinded the minds of unbelievers, so that they cannot see the light of the gospel of the glory of Christ…” 2 Corinthians 4:4. However, when Christ and His Church will reign on earth, then mankind will have their eyes opened for the first time. Then they will have their first opportunity to understand and accept Jesus. (“A new heart also will I give you, and a new spirit will I put within you: and I will take away the stony heart out of your flesh, and I will give you an heart of flesh.” Ezekiel 36:26)
You mentioned the “great white throne” in your question. I assume you are referring to Rev. 20:11 which says, “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.” This verse is part of a picture of what happens after the 1,000 years of Christ’s kingdom.
Revelation 20 is a prophecy of Christ’s 1,000 year kingdom and the “little season”. Revelation 20 acts like a bookend – it describes the beginning and end of Christ’s kingdom.
Revelation 20:1-6 tells us that Satan will be bound “to keep him from deceiving the nations.” Also, those “beheaded for the witness of Jesus” – the faithful Church or believers – will reign as kings and priests with Jesus for a thousand years. Who and what will the Church be reigning over? All of mankind and the Earth.
Revelation 20:7-15 tells us what happens “when the thousand years are expired.” What is missing in Revelation 20 is the description of what happens in between these two points. While Satan is bound during this 1,000 years, all of the dead will be resurrected here on Earth. After their resurrection, each man, woman, and child will begin to learn about God and righteousness.
We are promised that there will be a “restoration of all things” (Acts 3:21). That restoration will include mankind. Jesus “gave himself a ransom for all” (1 Timothy 2:6), and all are promised a resurrection – “all that are in the graves shall hear his voice and shall come forth” (John 5:28-29). Notice that it does not say a few or only the believers will be resurrected, but all will be resurrected.
This is a chance for all sinners. In Isaiah 35 we are told that the lame man will leap, the eyes of the blind will be opened, and the ransomed of the Lord will walk up a highway of holiness. Jeremiah 31:34 says all will have a knowledge of God. Christ’s kingdom will be full of healing and learning for all of those resurrected on Earth.
By the end of the 1,000 year kingdom of Christ, all people will have been resurrected and learned fully of God. Then comes the “little season,” a time when Satan will be set loose and allowed to tempt mankind one last time. Based on this last test, man will have the choice to follow God or follow Satan. Jesus (the one on the “great white throne”) will judge each person. Those who follow Satan will be destroyed. Those who follow God will have everlasting life. This is the first, real chance that all people have to live in harmony with God for eternity.