If an OBE is the situation that the soul leaves the body for a while, could this be possible as the Catholic Church states that body and soul are actually one entity.
Etymologically, "ecstasy" means "to stand outside of oneself," which could be what's meant by "outer body experience."
Ecstasy is, according to Fr. John Hardon, S.J.'s Catholic Dictionary:
In general, the state of being beside oneself through some overpowering experience. As a mystical phenomenon, it includes two elements, one interior and the other exterior. The invisible element consists in the mind being riveted on a religious subject. The corporeal aspect means that the activity of the senses is suspended, so that not only are external sensations unable to influence the soul, but these sensations become very difficult to awaken. Many saints have received ecstasies as a supernatural gift from God, although ecstasy of itself is not a criterion of holiness. (Etym. Greek ekstasos; from ex, out + histanai, to cause to stand: existanai, to derange.)
(cf. also the Catholic Encyclopedia's "Ecstasy" entry)
Many saints (e.g., St. Teresa of Ávila, St. Catherine of Siena, et al.) have experienced ecstasy where their bodies look as though they are dead, but they are really rapt in divine contemplation. St. Paul, for example, seems to have had an ecstasy, and he seems to have described a man who had ecstasies (2 Corinthians 12:2-4):
I know a man in Christ: above fourteen years ago (whether in the body, I know not, or out of the body, I know not: God knoweth), such a one caught up to the third heaven. And I know such a man (whether in the body, or out of the body, I know not: God knoweth): That he was caught up into paradise and heard secret words which it is not granted to man to utter.
It is possible, philosophically.
Keep in mind that a person can experience something that isn't reality. Reality is that which actually is- regardless of perspective, perception, or experience. To experience something, or to have the feeling of having had an experience, is different from an event actually occurring.
Paul's description, as pointed out by Geremia, is likely referring to himself- in which he experienced something but didn't know if it was bodily or non-bodily. This language assumes that both are possible. If your perspective is that the Bible is true and fact, and an authoritative description of an event is recorded, then the conclusion must be that it is possible to be reality, and not just experience.
I performed a cursory search through the Catechism of the Catholic Church on Vatican's website, and didn't find any direct results. You may be able to find related articles that indirectly address the issue.