The event establishes the Holy Ghost as a distinct Person of the Trinity, but it can't establish the eternal relationship of the Holy Ghost to the other Persons of the Trinity, since it is a temporal event.
My two cents, anyway.
I am out on a limb here, since I did not read this anywhere. But this is my speculative thinking.
I see a danger in drawing a bright line between temporal events and eternal relations. We don't have a mythical god who first defeated Gilgamesh, then married Brahmaputra, then created mankind, etc. True, we have the Creation, but our eternal God permeates it, so temporal events are visions of His divine eternal essence. Such bending and collapsing the sequence of time is, for example, necessary to explain the prefigurement of later temporal events in the earlier ones, and of course, the Real Presence of the Eucharist.
In other words, when we separate the temporal from the eternal, we rob ourselves of a deeper understanding. Christ breathing the Holy Ghost is an event that happened in time, but it is also a timeless image of the Triune Eternal God in operation.