Short Answer

Yes, the people alive on the last judgment will go, body and soul, into their final destination, and thus not experience a separation of the body and the soul, i.e. death.

Long Answer

What is death?

Death is understood in the Catholic faith as a separation of the soul and the body. As Father John Echert writes:

At the moment of death, the soul is separated from the body and no longer sustains order within the natural body

What happens upon death?

When someone dies, they undergo particular judgment defined by the Catholic Encyclopedia as:

The Catholic doctrine of the particular judgment is this: that immediately after death the eternal destiny of each separated soul is decided by the just judgment of God. Although there has been no formal definition on this point, the dogma is clearly implied in the Union Decree of Eugene IV (1439), which declares that souls leaving their bodies in a state of grace, but in need of purification are cleansed in Purgatory, whereas souls that are perfectly pure are at once admitted to the beatific vision of the Godhead (ipsum Deum unum et trinum) and those who depart in actual mortal sin, or merely with original sin, are at once consigned to eternal punishment, the quality of which corresponds to their sin (paenis tamen disparibus). The doctrine is also in the profession of faith of Michael Palaeologus in 1274, in the Bull "Benedictus Deus" of Benedict XII, in 1336, and in the professions of faith of Gregory XIII and Benedict XIV.

After the particular judgment, their soul will be in the condition of eternal suffering (Hell), eternal happiness (Heaven), or a purging period for temporal punishment due to sin (Purgatory) then eternal happiness. Eternal happiness is eventually guaranteed when a soul reaches purgatory since no soul in purgatory ends up in Hell according the the Catechism of the Catholic Church:

1031 The Church gives the name Purgatory to this final purification of the elect, which is entirely different from the punishment of the damned. The Church formulated her doctrine of faith on Purgatory especially at the Councils of Florence and Trent. The tradition of the Church, by reference to certain texts of Scripture, speaks of a cleansing fire

As for certain lesser faults, we must believe that, before the Final Judgment, there is a purifying fire. He who is truth says that whoever utters blasphemy against the Holy Spirit will be pardoned neither in this age nor in the age to come. From this sentence we understand that certain offenses can be forgiven in this age, but certain others in the age to come.

Once a person faces particular judgment, there is no changing that judgment as Father Paul K. Raftery writes:

The state of the dead up to this point [after particular judgement] had been one of souls abiding in separation from the body. But at the general judgment this separation of body and soul will be for ever ended. From this moment on men will have that union of body and soul God always intended for them. However, the appearance of the body for these two groups will be vastly different. The bodies of the blessed will be radiant with divine light, but those of the condemned will manifest the twisted and dark soul that is within (See Suppl. 75, 2, ad 3). Whatever the state of the soul is, that the body will reveal.

What happens at the last judgment?

At the last judgment, the souls of the dead will be reunited with their bodies, and the consequences of their actions will be made known to all according to the Catechism paragraph 1038:

1038 The resurrection of all the dead, "of both the just and the unjust," will precede the Last Judgment. This will be "the hour when all who are in the tombs will hear [the Son of man's] voice and come forth, those who have done good, to the resurrection of life, and those who have done evil, to the resurrection of judgment." Then Christ will come "in his glory, and all the angels with him. . . . Before him will be gathered all the nations, and he will separate them one from another as a shepherd separates the sheep from the goats, and he will place the sheep at his right hand, but the goats at the left. . . . And they will go away into eternal punishment, but the righteous into eternal life."

and paragraph 678 respectively:

678 Following in the steps of the prophets and John the Baptist, Jesus announced the judgment of the Last Day in his preaching. Then will the conduct of each one and the secrets of hearts be brought to light. Then will the culpable unbelief that counted the offer of God's grace as nothing be condemned. Our attitude to our neighbor will disclose acceptance or refusal of grace and divine love. On the Last Day Jesus will say: "Truly I say to you, as you did it to one of the least of these my brethren, you did it to me."

So how does the last judgment apply to those who are still living?

The same happens for the living at the time, and they will NOT die (and thus, strictly speaking, not face particular judgment), but rather directly undergo the last judgment and be sent to their final condition, body and soul, for eternity.

The parameters that apply to both the living and the dead, however, will be identical, save that those living at the time of the last judgment will not need to have their soul reunited with their body.

And thus we go full circle. Your reading from 1 Thessalonians confirms this:

Then we who are alive, who are left, will be caught up together with them in the clouds to meet the Lord in the air, and so we will always be with the Lord.