Yes. I have been able to find two letters, one related to the calling of the Council of Nicea and the other related to the judgment of the Council of Constantinople, where the word "persons" is used to describe the relations within the Godhead.
Council of Nicea (325)
First, some background. Alexander of Alexandria's conflict with Arius was the impetus for the council, as described by Khaled Anatolios in Retrieving Nicaea (page 42):
Arius and Alexander could not reconcile their differences over how to conceive the relation between the Father and the Son, however, and Arius was excommunicated from the Egyptian church sometime in the early 320s. Both Arius and Alexander appealed to surrounding bishops for support, and in response to the expanding controversy, the emperor Constantine convened the Council of Nicaea in 325.
One of Alexander's appeals mentioned above, a 324 letter to fellow bishop Alexander of Constantinople explicitly affirmed the personhood of the Son and implied the personhood of the Father:
But that the Son of God was not made "from things which are not," and that there was no "time when He was not," the evangelist John sufficiently shows, when he thus writes concerning Him: "The only-begotten Son, who is in the bosom of the Father." [John 1:18] For since that divine teacher intended to show that the Father and the Son are two things inseparable the one from the other, he spoke of Him as being in the bosom of the Father. Now that also the Word of God is not comprehended in the number of things that were created "from things which are not," the same John says, "All things were made by Him." For he set forth His proper personality [another translation says, "He also shows that he is a unique person"], saying, "In the beginning was the Word, and the Word was with God, and the Word was God. All things were made by Him; and without Him was not anything made that was made." [John 1:1-3]
Later in the same letter, he appears to affirm the personhood of both:
"I and My Father are one," [John 10:30] which indeed the Lord says, not as proclaiming Himself to be the Father, nor to demonstrate that two persons are one; but that the Son of the Father most exactly preserves the expressed likeness of the Father.
Later still, he strongly implies the personhood of the Spirit:
Besides the pious opinion concerning the Father and the Son, we confess to one Holy Spirit, as the divine Scriptures teach us; who has inaugurated both the holy men of the Old Testament, and the divine teachers of that which is called the New.
Council of Constantinople (381)
A letter written by the bishops gathered at Constantinople uses the term "persons" and affirms its consistency with the original Nicene Creed:
What we have undergone -- persecutions, afflictions, imperial threats, cruelty from officials, and whatever other trial at the hands of heretics -- we have put up with for the sake of the gospel faith established by the 318 fathers at Nicaea in Bithynia. You, we and all who are not bent on subverting the word of the true faith should give this creed our approval. It is the most ancient and is consistent with our baptism. It tells us how to believe in the name of the Father and of the Son and of the holy Spirit: believing also, of course, that 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. So there is no place for Sabellius's diseased theory in which the hypostases are confused and thus their proper characteristics destroyed. Nor may the blasphemy of Eunomians and Arians and Pneumatomachi prevail.
The above translation of the bishops' letter is originally from Decrees of the Ecumenical Councils by Norman Tanner. Read the relevant pages for yourself (hat-tip to Susan), which include the original Greek along with a Latin translation.
In the letters quoted above, the word "person" is a translation of the Greek prosopon. R.P.C. Hanson explains in The Search for the Christian Doctrine of God (pg. 183) that "for at least the first half of the period 318-381," which includes the time of the first council, "and in some cases considerably later, ousia and hypostasis are used as virtual synonyms." This led to Nicea's anathematization of those who say that the Father and the Son are "of a different hypostasis." It took the genius of the Cappadocian Fathers to standardize the terminology so that "the distinction between ousia and hypostases is the same as that between the general and the particular," and therefore that hypostasis would become synonymous with prosopon.