Not really possible. Even before Dax was brought into existence, Overvoid was shocked by the Flaw and made the Orrery to contain it and prevent it from spreading further. It also chose to define itself in relation to the Flaw, forming a duality with it.
The bolded part is untrue, Dax was not brought into existence, but was rather explicitly an
extension of Monitor designed to fit in the Flaw.
We do understand how it is essentially impossible to describe the Overvoid in any sense of the word, seen in the Arthurmag interview where Grant says that God would essentially resolve all thoughts, including thoughts regarding its own self. The Book of Limbo, which is quite literally
all possible books shows this, by acknowledging how it is all possible descriptions, as well as
the story that has all stories within it, but then explicitly calling the Overvoid to be
beyond thought.
By that very metric, to even call the Overvoid an "immaculate intelligence" or "Monitor" you, in fact, put it within the bounds of thought, which it explicitly isn't dependent or limited to. That, on it's own, is a debunk to the idea of the Overvoid being within any duality via the Multiversity scans, because whatever the Cave understands of the Overvoid is not even the full scope of the Overvoid, you would be assuming that an intentionally limited perspective on the Overvoid is in a duality, when even just saying that, makes it a "thought", and thus, the actual full, undefinable scope of the Overvoid, stays non-dual all the same.
This is seen in FC, when Mandrakks contamination also ends up in the Overvoid being described as "infected", even though, we know very well that Mandrakk is the part of it that took the "contamination", and by extension, considering the contamination arised specifically out of "Monitor Examination" and the extension of itself that was designed to fit in the Flaw, the actual unextended Mandrakk is what we see in the Cave and in the Book of Limbo, the part of it that viewed it as a "flaw" in the first place. This illustration should explain it better.
Moreover, considering Mandrakk a "part" of the Overvoid makes the notion of true duality even more challenging to justify.
No, not really. I'm not really arguing for a monadic type entity with absolutely no parts so this is unrelated, Eternitys transduality for example is far higher then the transduality I'm proposing for the Overvoid, but definitely is seen having "parts" of itself throughout the years.
Eitherway, this argument falls apart when we recognise the idea that Mandrakk as a Monitor
is essentially a thought of the Overvoid, as well as explicitly within a
duality that falls apart right before its unity. Combine that with the Kid Eternity scans that describe the fall and rise of consciousness from non-duality to duality, and Mandrakk is no more then an emanation of the Overvoid, the emanation that felt that the Void was contaminated. So again, "part" here is very metaphysical.