Yes, Holy Communion unites our souls to Jesus’ divine and human natures. It is an article of faith that the Blessed Sacrament of the Altar is truly, really, and substantially the Body and Blood of Christ, together with His soul and divinity. Therefore, when we receive Holy Communion, we receive the real, physical Body and Blood of Christ, together with His soul and His divinity, veiled under the appearances of bread and wine.
Put another way, during Holy Communion, we receive the same Body of Jesus which He took from His most pure Virgin Mother, and which arose in glory from the tomb; His Precious Blood, with which He redeemed us—one drop of It would have been enough to redeem a thousand worlds!—and His most sacred soul, the abode of graces and virtues in absolute perfection.
We share in Christ’s life as the Divine Word and as the only Son of the Father. We receive the life the Father gives to the Son from all eternity. We can possess His divinity in our souls at all times by remaining in the state of grace; but it is only at the time of Holy Communion that we enjoy the great privilege of being intimately united with the human nature of our Lord.
The three divine Persons are already in us by grace, but at the moment of Communion they are present within us in a special manner. As we are then sacramentally united to the Incarnate Word, the three divine Persons are also, through Him and by Him, united to us, and They love us as the Word Incarnate, Whose members we are. When we carry Jesus in our hearts, we also bear the Father and the Holy Spirit with Him. Thus, Holy Communion is a foretaste of Heaven.
To receive our Lord in Holy Communion is the most wonderful thing that can happen to us, because it means having the God-man, Jesus, in our own hearts. The Holy Eucharist is the greatest and the holiest of the sacraments, because it is our Savior Jesus Christ Himself, God Who became man for our Salvation.
Holy Communion also brings about a special union between us and the three divine Persons of the Holy Trinity. Jesus said, “If a man loves me, he will keep my word, and my Father will love him, and we will come to him, and make our home with him” (John 14:23).