Yes. The Catholic Faith understands procession as existing in God because Divine Scripture uses, in relation to God, names which signify procession.
Procession is not to be understood from what it is in bodies, either according to local movement or by way of a cause proceeding forth to its exterior effect.
Some have understood it in the sense of an effect, proceeding from its cause; so Arius took it, saying that the Son proceeds from the Father as His primary creature, and that the Holy Ghost proceeds from the Father and the Son as the creature of both.
Others take this procession to mean the cause proceeding to the effect, as moving it, or impressing its own likeness on it; in which sense it was understood by Sabellius, who said that God the Father is called Son in assuming flesh from the Virgin, and that the Father also is called Holy Ghost in sanctifying the rational creature, and moving it to life.
Careful examination shows that both of these opinions take procession as meaning an outward act; hence neither of them affirms procession as existing in God Himself.
Whenever we understand, by the very fact of understanding there proceeds something within us, which is a conception of the object understood, a conception issuing from our intellectual power and proceeding from our knowledge of that object. This conception is signified by the spoken word (vox); and it is called the word of the heart (verbum cordis) signified by the word of the voice (verbo vocis).
Therefore procession is to be understood by way of an intelligible emanation (emanationem intelligibilem); for example, of the intelligible word which proceeds from the speaker, yet remains in him.