The Catechism of the Catholic Church has this to say on drugs:
The use of drugs inflicts very grave damage on human health and life. Their use, except on strictly therapeutic grounds, is a grave offense. Clandestine production of and trafficking in drugs are scandalous practices. They constitute direct co-operation in evil, since they encourage people to practices gravely contrary to the moral law.
However, the Church doesn't necessarily have a position on whether any particular substance is or is not a drug. In 2001, the Pontifical Council for Health Pastoral Care produced a document titled Church: Drugs and Drug Addiction, the preface and table of contents of which are available on the Vatican website. According to the table of contents, the section titled "The Products" covers glue and other solvents, cannabis, cocaine, ecstasy, and heroin. Clearly, these are not the only available substances that might be classified as "drugs"; but at the time the Council obviously considered them the most important to deal with directly. Since this is a pastoral document, it's obviously not intended to give a comprehensive list of how to deal with all drugs, but how to deal with the most important, or most commonly encountered, or most harmful ones.
How then might the Church approach the question of whether a given substance constitutes a "drug"? One consideration is whether the civil authorities consider it to be a drug:
Those subject to authority should regard those in authority as representatives of God, who has made them stewards of his gifts: "Be subject for the Lord’s sake to every human institution.... Live as free men, yet without using your freedom as a pretext for evil; but live as servants of God." [1 Peter 2:13, 16]
(Catechism of the Catholic Church, paragraph 2238)
The civil authorities are to be obeyed unless "they are contrary to the demands of the moral order, to the fundamental rights of persons or the teachings of the Gospel." It is not clear that classifying a particular substance as a drug, or a non-drug, meets this criterion.
Further, one can look again at the Catechism's paragraph 2291 cited above. This is placed in the Catechism's discussion of the fifth commandment: You shall not kill. From this commandment, we can deduce the importance not only of human life but of health which supports life; it is for this reason that the use of drugs in a non-therapeutic manner is a grave evil. And this, finally, may be a reason for considering it a drug: there appear to be no non-therapeutic uses for it.
With respect to its supposed positive spiritual effects, the Church is very clear that the way to approach spiritual life—to come closer to God—is through prayer.
Christian prayer is a covenant relationship between God and man in Christ. It is the action of God and of man, springing forth from both the Holy Spirit and ourselves, wholly directed to the Father, in union with the human will of the Son of God made man.
In the New Covenant, prayer is the living relationship of the children of God with their Father who is good beyond measure, with his Son Jesus Christ and with the Holy Spirit.
For this reason, it would not be surprising if the Church were to formally condemn the use of DMT and similar psychedelic drugs, independent of civil authority; however, it appears that no such statement is forthcoming, nor likely to be.