Yes, it is! :)
I don't know how we got on this topic of Hypostases, but the original idea was that grace is God's uncreated energy, which God conveys upon us through the Hypostatic interaction with us. Again, God is seen differently and separately in terms of Hypostases, the Father being distinct from the Son and both being distinct from the Spirit, yet all Three are fully God, and individiuble.
The idea of God's grace being the uncreated means rather than created means of our salvation was something the Church knew even as early as 2nd century, when St. Ignatius wrote about it in those terms. The trouble in the west began with none other than our dear St. Augustine, who disagreed with hesychasts on our ability to reach theosis through prayer and see the uncreated light of God. Apparently the Church did not have any issues with uncreated grace as seen by Ss. Ignatius, Basil, and Nazienzos prior to that.
I don't think the West disagrees that a mystic can reach theosis and "see" God through contemplative prayer. St. Augustine himself was a mystic. I think where I have problems with is on several issues:
First, I bring up hypostases (persons) and the Trinitarian formulas because whenever one discusses Christological issues, (which "energy" appears to be), then naturally, we must look at our Trinitarian definitions. And at Chalcedon, it was clear that it is the nature, not the person that acts. Also, the Great Councils determined that the nature, God's Essence, is entirely in each Hypostasis. Thus, if Christ comes to man as at Mt. Tabor, God's Essence is FULLY PRESENT, not just His Energy.
The second issue is how we "know" and contact God's nature. You are correct that both the East and the West has a patristic background that notes that man cannot comprehend the essence of God. Your quote from Basil is one of several that I found among the Cappadocians and St. John Chrysostom, but also St. Augustine as well. The thing I see here is the degree of "knowledge" that man can possess and the NEED of an energy. Here are some examples:
No one knows the Father except the Son". What then? Are we all in ignorance? Perish the thought! But no one knows Him as the Son knows Him. Many have seen Him to the extent of the vision permitted them, but no one has seen His essence; so too, all know God, but what His essence is no one knows, except only the One begotten of Him. For by "knowledge" He means the exact notion and comprehension such as the Father has in respect to His Son: As the Father knows Me, so do I know the Father. (St. John Crysostom, Homilies on the Gospel of John, 15, 1)
Again,
"Why does John say "No one has ever seen God"? So that you might learn that He is speaking about perfect comprehension of God and about precise knowledge of Him ...When, therefore, you hear that "no one has ever seen God", consider it the same as hearing that no one can know God in an utterly perfect manner, as to His Essence...When, therefore, the Prophet says that although God was condescending, [the Seraphim and Cherubim] could not bear to look at Him, it means nothing else but that they were not able to have a clear knowledge and an accurate comprehension of Him, nor did they dare to gaze intently upon His pure and perfect Essence, nor even upon this condescension. For to gaze intently is to know." (St. John Crysostom, Homilies against the Anomoians and on the Incomprehensible Nature of God, 4, 3)
Thus, to "see" means to fully comprehend - not that we never contact God's Essence.
And St. Basil writes about knowledge:
"But if, in our teaching, anyone say that knowledge comes before faith, I raise no objection, rather, taking knowledge as referring to the knowledge that is within the limits of human comprehension". (St. Basil, Letter 235, 1 - the one immediately following the one he speaks about "knowing" God's essence is not possible)
"What God is in nature and essence, no man has ever yet discovered nor can discover...It seems to me that this is the solution to that whole philosophical problem of our being about to know even as we have been known. But in our present mode of existence all that is apparent (about God's essence) to us is but an effluence, like a little radiance from a great light." (St Gregory of Nazianz, Second Theological Oration, 28,17)
From these and the writings of the mystics such as St. Symeon the New Theologian, I think it is more proper to say that man's knowledge of God's essence is limited to Its existence. It is incomprehensible. But it is "seen" through the "eyes" of the mystic. Man not only "sees" God's action, but His Essence - in an incomprehensible manner. That light is not an energy, alone, but God's nature, God's essence itself, also. But this essence is totally incomprehensible to the intellect. None have been able to describe it beyond a spiritual knowledge of its existence. Thus, I don't see the necessity of calling Christ's abiding presence an "energy" alone. When God comes, He comes completely. His Action and His Nature. We contact it - however incomprehensible it might be to us.
Regards