No. That passage is clear about the goats going to everlasting fire so that is directly related to the LOF punishment found in Rev 20 and that isn't held on Earth per verse 11.
I believe you are Premill from your posts so we don't believe Jesus does the LOF judging for the unsaved at the second coming anyways so that is another clue the passage in Matthew 25 is not speaking about the timeframe of the second coming. Again, verse 11 is key to the location and a non-Earthly location means a coming to that place unrelated to the commonly known "second coming".
Matthew 25 is talking specifically to Israel, and the sheep are redeemed at that judgment, not prior to that judgment. These sheep are not the church. They are the redeemed of Israel to live on the earth during the Millennium. This is the Second Coming and Jesus is sitting as the King of Israel over the sheep and goats of Israel. Only a remnant of Israel is saved. Two thirds of Israel will be goats cast into the LOF at the Second Coming during the first 6 Trumpets.
This is All the lost of Israel scattered among all the nations since 720 BC. Also all who have been scattered since then. Hitler tried to exterminate all who lived in Germany and who he could find across Europe. Many were killed in 70AD. But that did not remove all from the earth. Only at the Second Coming will they all be gathered back as one nation. You are interpreting Matthew 25 thinking it is about saved and lost. No, it is about all of Israel being returned, and only a remnant survive.
Saved Israel as part of the church all went to Paradise at the rapture. The sheep and goats are Israel still on earth after the rapture and Second Coming. You cannot apply this to the church and lost. This is not the GWT judgment after the Millennium. These are those who live on earth during the Millennium. But not all of Israel make it. That is why it is Jacob's trouble known as the Great Tribulation with nothing compared to this time period.
I think people have the 10 virgins wrong as well. The 5 virgins are Israel who have followed Christ. The other 5 are Israel who have followed Moses and the Law. Still all about Israel and not about half the church are unbelievers and the other half are believers.
Either you are the church or not. Many who go to church are nothing. They have relied on what people tell them they are, and never made any personal decision themselves to follow Jesus Christ. That is not what Matthew 25 is about. Many of Israel will leave as the church at the rapture. The rest will be sorted as sheep and goats. Many sitting in church pews left behind will all be decieved by Satan and take the mark or wise up and chop their head off. Or all be killed in the winpress of God's wrath along with the rest of humanity. There is still the wheat harvest during the 7 Thunders mentioned in Matthew 13. Jesus will be sowing the Gospel on earth and will redeem many from all nations. That is why people are warned not to listen to false christs. But Satan will be working as well to keep people deceived.
Satan could not work openly between the baptism of Jesus and the time of the Cross. But at the Second Coming, Satan will work out in the open. All will know he has always existed. Many will still choose him over Jesus and God sitting on the GWT. All on earth will see God sitting on the GWT after the 6th Seal. No one on earth will have the excuse they don't know what is going on. There will be no spiritual blindness.
No one will say after the 6th Seal, God is talking about a non-earthly location. The GWT has always been on earth and in heaven. No one can see it because they are spiritually blind. We have been told that heaven is the throne, and the earth is the foundation. No one can build a building big enough to put the GWT into. It would also seem to be not exactly a solid physical throne, but white could mean a bright light, that our dead flesh eyes cannot even look at it unless they are consumed. Worse than looking at the sun. We know they can see it, because John wrote:
"And the kings of the earth, and the great men, and the rich men, and the chief captains, and the mighty men, and every bondman, and every free man, hid themselves in the dens and in the rocks of the mountains; And said to the mountains and rocks, Fall on us, and hide us from the face of him that sitteth on the throne."
All they could really see without going blind was that God had a face. They wanted to get away from the GWT as far as they could.
So one cannot say Matthew 25 and the GWT is only some event that happens off earth after creation is gone. From the 6th Seal until the end of the Millennium the GWT will be fully seen as part of heaven and earth. Then after the Millennium, creation will cease to exist, and only the GWT will remain. It is not found on the NHNE. God will reside in the New Jerusalem which will be bigger than the GWT. The LOF will be the only part of current creation left. But how the LOF even works or consist of is still unknown, except the name. It is brought into reality at the Second Coming in conjunction with the baptism of fire at the 6th Seal per 2 Peter 3.
Just like the oceans are a huge Lake of Water resulting from the Flood. The LOF will be the result of the judgment of fire this time instead of water.
Yes, the dead stand in judgment after this creation ends. But the living can still be cast into the LOF at any point after the 7th Seal is opened. People really don't seem to grasp how bad things will get after the 6th Seal. Then they get even worse if Satan gets 42 months of the abomination of desolation. They want to procrastinate all the bad stuff and then think it will all be over in a blink of an eye. During the Trumpets, people will want to die and try to die, but cannot, until God lets them die.
"And in those days shall men seek death, and shall not find it; and shall desire to die, and death shall flee from them."
So being beheaded cannot even happen until after the 7th Trumpet has sounded. And then only if there is a 42 month extension.