No. Here's this from Wikipedia; it'll tell you the meaning of "person."
Hypostasis (philosophy and religion) - Wikipedia, the free encyclopedia
Are you talking about this paragraph?
In Early Christian writings it is used to denote "being" or "substantive reality" and is not always distinguished in meaning from ousia (essence); it was used in this way by Tatian and Origen, and also in the anathemas appended to the Nicene Creed of 325. See also: Hypostatic union, where the term is used to describe the union of Christ's humanity and divinity. The term has also been used and is still used in modern Greek (not just Koine Greek or common ancient Greek) to mean "existence" along with the Greek word hýparxis (ὕπαρξις
and tropos hypárxeos (τρόπος ὑπάρξεως
, which is individual existence.
Hmmm, there goes the whole "person, not being" argument out the window. It would be thus 3 different existences, not 1 existence made up of 3 beings but 3 separate existences. That would be what "Substantive reality" would imply. The idea of them being "unified" is not however substantiated.
So therefore:
The Christian view of the Trinity is often described as a view of one God existing in three distinct hypostases/personae/persons. The Latin "persona" is not the same as the English "person" but is a broader term that includes the meaning of the English "persona
It is in fact 3 different beings in this view.
Now if they're trying to compare it to the Neoplatonist use of the term, in that Body, Spirit, and Soul make up one Being, that's entirely different, since the Soul and Spirit are not different "persons" with independent wills and minds, they are components. Likewise, the Soul and Spirit are not the "Son" of the Body. The original use of Hypostasis would be more like how a machine works, except with inanimate parts. The leap from saying that "Mind (soul), Body, and Spirit" somehow translates to Son, Father, and Spirit making up one Being in unity has a big Phase 2: ? in it.
It's simply an irreconciable position. If it was reconcilable, it wouldn't be "Too complicated for the human mind to understand".
As Muffled said, the concept of "person" in this unique usage of the term seems to only have meaning to "Theologians", and even then, this meaning is "Too complicated" for their poor, frail human minds, since it's obviously so obtuse that humans must simply accept how it applies to the doctrine without understanding it in the first place.
Now the Arian idea, not only has no inconsistencies or vague, undefined wordsmithing or fabricated deviances from original Platonic Metaphysical concepts, it matches completely up with both Philo and the Targums' idea of the Jewish understanding of the Logos.