Yes and no. It depends on how this expression is understood. First, let’s consider the erroneous interpretation of this expression.
It is a dogma of the Catholic Faith that the Three Persons of the Trinity are consubstantial. They have the very same substance or essence or being or nature (each of those words denoting the same thing). In other words, God has only one Divine Nature, and each of the Three Persons fully possesses that one Nature. So whatever can be truly said about the Divine Nature, can be truly said about each of the Three Persons.
Each Person is all-knowing because the Divine Nature is all-knowing. The knowledge of God is not only in the Son. The claim that the knowledge of God is only in the Son is heresy, because it denies that all Three Persons are consubstantial.
God is love, by His very Nature. So each Person of the Trinity is truly Love. The love of God is not only in the Spirit. The claim that the love of God is only in the Spirit is heresy, because it denies that all Three Persons are consubstantial. God is Love by His very Nature, so each Person must be Love.
The Holy Spirit is NOT the love between the Father and the Son IN THE SENSE that all the love the Father has for the Son, and vice versa, is not in either of those Persons, but is only in the Spirit. We cannot attribute any aspect of the Divine Nature to one Person only, to the exclusion of the other two Persons.
So when we speak about love as the essence or nature of God, “the Father and the Son love each other not by the Holy Spirit, but by their essence”, meaning by the one Divine Nature. [Aquinas, Summa Theologica, Q 37 A 2]. What Saint Thomas is saying is that the love of the Father for the Son, and the love of the Son for the Father, is part of the very nature of God, and so it is not exclusively found in the Spirit. The love of the Father for the Son is in the Father, and the love of the Son for the Father is in the Son, and the love of the Spirit for the Father and Son is in the Spirit. So the love of each Person is in that Person. Each Person loves the other Persons of the Trinity, as their very essence. For love is of the Divine Nature and the Three Persons are consubstantial.
In what sense, then, can we say that the Holy Spirit is the Love between the Father and the Son? This assertion IS TRUE as a description of the procession (also called spiration) of the Holy Spirit from the Father and the Son. Each Person truly is Love by his very Nature; one and the same Nature is fully possessed by each. But the procession of the Spirit from the Father and the Son can be described (by way of analogy) as a spiration of love, as if the Person of the Spirit were an expression of love so full as to be a Person. Similarly, we say that the Son is like a Word spoken by the Father, a Word so full as an expression of the knowledge of the Father as to be a Person. But these things are said by way of analogy. Knowledge is not only in the Son, and Love is not only in the Spirit.
The Ecumenical Councils teach:
Nicea I: Jesus Christ, the Son of God, born of the Father, that is, from the substance of the Father, God from God, light from light, true God from true God, begotten not made, of one substance with the Father (which the Greeks call “one in being”)
Constantinople I: the Father, the Son and the holy Spirit have a single Godhead and power and substance, a dignity deserving the same honour and a co-eternal sovereignty, in three most perfect hypostases, or three perfect persons.
Ephesus: Jesus Christ, the only begotten Son of God perfect God and perfect man of a rational soul and a body, begotten before all ages from the Father in his godhead, the same in the last days, for us and for our salvation, born of Mary the virgin, according to his humanity, one and the same consubstantial with the Father in godhead and consubstantial with us in humanity, for a union of two natures took place.
Chalcedon: When God is believed to be both almighty and Father, the Son is clearly proved to be co-eternal with him, in no way different from the Father, since he was born God from God, almighty from the Almighty, co-eternal from the Eternal, not later in time, not lower in power, not unlike in glory, not distinct in being.
Constantinople II: the Father, Son and Holy Spirit have one nature or substance … they have one power and authority … there is a consubstantial Trinity, one Deity to be adored in three subsistences or persons.
Constantinople IV: we declare our belief in one God, in three persons consubstantial, divine and autonomous…. We confess, indeed, God to be one, unique in respect of substance, but threefold or three if we are speaking of him in respect of persons, and we declare … that he is alone, ever existing without beginning, and eternal, ever the same and like to himself, and suffering no change or alteration, that he exists as the maker and source of all beings endowed with intelligence and feeling.
Lateran IV: We firmly believe and simply confess that there is only one true God, eternal and immeasurable, almighty, unchangeable, incomprehensible and ineffable, Father, Son and holy Spirit, three persons but one absolutely simple essence, substance or nature. The Father is from none, the Son from the Father alone, and the holy Spirit from both equally, eternally without beginning or end; the Father generating, the Son being born, and the holy Spirit proceeding; consubstantial and coequal, co-omnipotent and coeternal….
Finally the only-begotten Son of God, Jesus Christ, who became incarnate by the action of the whole Trinity in common and was conceived from the ever virgin Mary through the cooperation of the holy Spirit, having become true man, composed of a rational soul and human flesh, one person in two natures, showed more clearly the way of life.
there exists a certain supreme reality, incomprehensible and ineffable, which truly is the Father and the Son and the holy Spirit, the three persons together and each one of them separately. Therefore in God there is only a Trinity, not a quaternity, since each of the three persons is that reality — that is to say substance, essence or divine nature-which alone is the principle of all things, besides which no other principle can be found. This reality neither begets nor is begotten nor proceeds; the Father begets, the Son is begotten and the holy Spirit proceeds. Thus there is a distinction of persons but a unity of nature. Although therefore the Father is one person, the Son another person and the holy Spirit another person, they are not different realities, but rather that which is the Father is the Son and the holy Spirit, altogether the same; thus according to the orthodox and catholic faith they are believed to be consubstantial…. Thus the Father and the Son and also the holy Spirit proceeding from both are the same reality.
Lyons II: We profess faithfully and devotedly that the holy Spirit proceeds eternally from the Father and the Son, not as from two principles, but as from one principle; not by two spirations, but by one single spiration.
Florence: the holy Spirit is eternally from the Father and the Son, and has his essence and his subsistent being from the Father together with the Son, and proceeds from both eternally as from one principle and a single spiration. We declare that when holy doctors and fathers say that the holy Spirit proceeds from the Father through the Son, this bears the sense that thereby also the Son should be signified, according to the Greeks indeed as cause, and according to the Latins as principle of the subsistence of the holy Spirit, just like the Father. And since the Father gave to his only-begotten Son in begetting him everything the Father has, except to be the Father, so the Son has eternally from the Father, by whom he was eternally begotten, this also, namely that the holy Spirit proceeds from the Son.
the holy Spirit is eternally from the Father and the Son, and has his essence and his subsistent being from the Father together with the Son, and proceeds from both eternally as from one principle and a single spiration.
Vatican I: the holy Spirit, the lord and the giver of life, who proceeds from the Father and the Son. Who together with the Father and the Son is adored and glorified: who spoke through the prophets.
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