Not to me. It's like saying of your spouse: "She's a bipedal primate belonging to the species Homo sapiens in Hominidae having a highly developed brain, capable of abstract reasoning, language, introspection, and problem solving."
It's descriptive and accurate but insufficient for your well-stated desire to "know exactly who we have that intimate relationship with, to know exaclty who that person is."
That's an accurate observation, but misses the mark. :) When the eastern Christians say they "know' him they think of Christ, the Christ know to the Church. There is no other God. Christ is it. When you see Christ you see the Father.
God is otherwise ineffable and all attempts to figure out the ineffable God (the Truth you are pursuing) are doomed to failure. And worshiping an ineffable God is like worshiping a stone. You can't have a relationship with a stone, or the sun, or some invisible, incomprehensible spirit.
As the Bible says, no one gets to the Father except through Christ. And Chirts is knowable (whether that is a historical Jesus or not is a different story), but knowable as far as the Christ known to the Church of the Seven Councils is concerned, and very real in a character sense. In fact, he is the role model of how to be saved (theosis). become Christ-like and you are saved. Do what he would have done and you are saved (cf Mat 25).
So, while the Church went out of its way to define the incomprehensible Trinity, let alone the ineffable God in his true nature, the Church does not deal the the divine Mystery except through praise and adoration. When it comes to dealing with God, the Church in the East deal exclusively though Christ, and he doe snot have to be described or understood or loved in any strange an incomprehensible way.