Does the Eastern Orthodox Church consider belief in the existence of Jesus' soul before the incarnation a heresy?
The question is imprecise. It can be read as asking the existence of Christ before His incarnation (which is about the divine person) or about the existence of His human soul before incarnation (which is about His human nature). If it's the former the answer is definitively no. Even Arius of Alexandria while denying the Son is of the same essence with the Father he never questioned that the Logos is exist prior to His incarnation. If it's the later the answer is affirmatively yes. At the Fifth Ecumenical Council of Constantinople (553) the heresy of eternal humanity of Christ is condemned:
If anyone asserts the fabulous pre-existence of souls, and shall assert the monstrous restoration which follows from it: let him be anathema.
First Anathema Against Origenism, Second Constantinople 553.
The confusion regarding the difference between what constitute a person and a nature. Jesus' human soul came into existence at the moment of His conception by Theotokos. Human soul is assumed by the Logos in His incarnation not prior. Why this is not the case? Because His humanity is not the proto-type of Adam, it's the other way around. His humanity was taken from Adam. He healed our humanity by assuming it. If He has His own humanity then our humanity is not healed because the fallen nature of Adam has not been assumed. This is why His human soul began to exist only after the conception not prior as argued by Origen.
A good friend of mine who is Eastern Orthodox answered this question for me - he said they DO believe Jesus was present BEFORE the incarnation (assuming I understand your question right). Hence the Hymn of the Only Begotten Son:
"O only begotten Son and Word of God,
Who, being immortal,
Deigned for our salvation
To become incarnate
Of the holy Theotokos and ever-virgin Mary,
And became man without change;
You were also crucified,
O Christ our God,
And by death have trampled Death,
Being one of the Holy Trinity,
Glorified with the Father and the Holy Spirit—
To not accept Christ as being present before incarnation would be heretical, as He is the Word of God and was present before creation, and through Him all things were created. See the beginning of John, for example. And some part that escapes my mind in Hebrews.
The greatest cause of confusion, and a progenitor of heresy in our Orthodox faith, is trying to describe eternal concepts using thinking and expression born in an existential experience bounded by the limits of time and space. For example, and the texts above are rife with these, when Jesse writes, "Christ's soul would have existed prior to the incarnation." The phrase "would have existed prior" implies time, but "christ soul" must be eternal and so has no "prior" or "would have" involved. St Silouan writes,
"Eternity is a unique act of Divine being, an act of incomprehensible fullness, which, being transcendent, embraces in one point all the dimensions of the created world [all creation]. Only the One God is eternal in substance. Eternity is not an abstraction, an entity existing separately, but is God Himself in His own Being. When it is God’s good pleasure to give man grace and make him a partaker in Divine life, man becomes, not only immortal in the sense of having his life endlessly prolonged, but beginningless, too, for the sphere of Divine life into which he is lifted has neither beginning nor end." (Sophrony, St Silouan the Athonite. p. 146. Emphasis added.)
Origen wrote of the pre-existence of Souls and was anathemized for it. On the line of time, even from the perspective of immortality, every soul has her beginning when she comes into being at conception; so Origen’s thoughts are correctly confronted. Yet, all time has its existence in the eternality of the mind of the One Who is Three, and so every created creature exists in the eternality of the Logos. Thus, in the Mind of the Immanent-Transcendent Supreme Being, creation exists in the timelessness of beginningless endlessness, and from this vantage, all creation is preexistent. This includes Immortality, immortal souls, and all creation. From this vantage Origen was ignorantly accused of heresy. John