His Second Coming, yes.
The Rapture, no. That is the point of pointing out the Scripture referring to His Return: both the wicked and believing are judged at His Return. Whereas in the First Resurrection we see only believers that have died raised to life again.
The wicked at that time, while they go into everlasting punishment, this everlasting punishment begins in Hades, not Gehenna/Hell.
Revelation 20:4-6 King James Version
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.
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.
Secondly, we do not see a focus on the living believing here.
Third, the "trumpet" is not the Last Trumpet Judgment. There is clearly a period of time after the Seventh Trumpet Judgment sounds. This unleashes the Seven Bowl Judgments.
Consider:
Exodus 19:16-20 King James Version
16 And it came to pass on the third day in the morning, that there were thunders and lightnings, and a thick cloud upon the mount, and the voice of the trumpet exceeding loud; so that all the people that was in the camp trembled.
17 And Moses brought forth the people out of the camp to meet with God; and they stood at the nether part of the mount.
18 And mount Sinai was altogether on a smoke, because the Lord descended upon it in fire: and the smoke thereof ascended as the smoke of a furnace, and the whole mount quaked greatly.
19 And when the voice of the trumpet sounded long, and waxed louder and louder, Moses spake, and God answered him by a voice.
20 And the Lord came down upon mount Sinai, on the top of the mount: and the Lord called Moses up to the top of the mount; and Moses went up.
Here we have a trumpet calling the people of God out of the camp. But we are not come unto Mount Sinai, but unto the Heavenly Jerusalem in the Rapture. Christ doesn't return in the Rapture, we are taken out.
Here is a trumpet that is specific to the Tribulation:
Zechariah 9:14-17 King James Version
14 And the Lord shall be seen over them, and his arrow shall go forth as the lightning: and the Lord God shall blow the trumpet, and shall go with whirlwinds of the south.
15 The Lord of hosts shall defend them; and they shall devour, and subdue with sling stones; and they shall drink, and make a noise as through wine; and they shall be filled like bowls, and as the corners of the altar.
16 And the Lord their God shall save them in that day as the flock of his people: for they shall be as the stones of a crown, lifted up as an ensign upon his land.
17 For how great is his goodness, and how great is his beauty! corn shall make the young men cheerful, and new wine the maids.
The reference to corn and alcohol again shows a physical kingdom after the Tribulation.
Here, Israel is the object of salvation, and that is physical salvation as well as eternal salvation (for only those born again will enter into that kingdom).
Now a "trumpet" relevant to the Rapture:
Revelation 4 King James Version
4 After this I looked, and, behold, a door was opened in heaven: and the first voice which I heard was as it were of a trumpet talking with me; which said, Come up hither, and I will shew thee things which must be hereafter.
It is a voice "as if it were the voice of a trumpet."
Isn't that what we see in regard to the trumpet?
1 Thessalonians 4:16 King James Version
16 For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God: and the dead in Christ shall rise first:
It is the Lord "shouting," calling His people out of the "camp," the "wilderness." And unlike the people of God at Sinai, we can go into the presence of God boldly based on Christ's Sacrifice.
Revelation 1:10-11 King James Version
10 I was in the Spirit on the Lord's day, and heard behind me a great voice, as of a trumpet,
11 Saying, I am Alpha and Omega, the first and the last: and, What thou seest, write in a book, and send it unto the seven churches which are in Asia; unto Ephesus, and unto Smyrna, and unto Pergamos, and unto Thyatira, and unto Sardis, and unto Philadelphia, and unto Laodicea.
It is "the last trump/et" because it is the sound that calls us out of this world.
Again, the Lord is never said to return in the Rapture, we are said to be called out. Snatched up.
In the Sheep and Goat Judgment, which takes place at the Lord's Return, it is the wicked that are "taken (out)" and the believers are left:
Matthew 24:27-28 King James Version
27 For as the lightning cometh out of the east, and shineth even unto the west; so shall also the coming of the Son of man be.
28 For wheresoever the carcase is, there will the eagles be gathered together.
Luke 17:34-37 King James Version
34 I tell you, in that night there shall be two men in one bed; the one shall be taken, and the other shall be left.
35 Two women shall be grinding together; the one shall be taken, and the other left.
36 Two men shall be in the field; the one shall be taken, and the other left.
37 And they answered and said unto him, Where, Lord? And he said unto them, Wheresoever the body is, thither will the eagles be gathered together.
The gathering of the eagles represents the carrion fowl that will feast upon the carcasses of the dead unbelievers. This is the Supper of the Great God, spoken of in Prophecy in both Old and New Testaments. This takes place at the end of the Tribulation, and it does not correspond to the Church being called out of the world.
And that is the problem that arises from trying to make the last trump the Seventh Trumpet Judgment: it just doesn't fit in with what we're told.
God bless.