Sorry no. A and Not A.
In a world where A exists everything outside of the set A is Not A. My disjunction is logically correct. You are excluding the middle and admitting to excluding the middle.
The Null position on whether or not a god exists is by definition outside of the set of those who believe that a god exists. If you ask me if I believe in god and I say I honestly don't know then that's NOT theism. It resides outside of the set of theism.
To argue logically our premises need to be based on propositions. Statements that are binary. IOW: They are either true or false. One trap of binary statements is that they often exclude the middle (including the null hypothesis). So, instead of "Bob's car is either red or blue" we change the statement to "Bob's care is either red or not red" (blue being a car that exists in the set that is not red). Got it?
Your homework, give me a proposition (true or false statement) that dos not exclude the null hypothesis?
Yeah, you missed and update that you wouldn't like still more (agnostic).
I choose not to follow your rules because they don't reflect reality, as they should. At least, not the reality I see. Like the car color, you want a binary propositon, but it is not a binary reality. Bob's car may be red, but all not reds are not equal. Bob's car is red or not red only tells you if Bob's car is red or not red, a very limited use choice. This is fine if you are only interested in red cars. If Bob's car model comes in 4 colors, his car is one of the 4, or a 5th self applied color, or a 6th where the color has been removed. Binary won't tell you the distribution of colors of the model.
You can live in a Belief / Not Belief world, if you choose. This means you will treat agnostics, atheists, and the unknown the same, and expect their choices that follow to be the same, which is not reality.
Reality says there is evidence on the existence of god, of people approaching the evidence, along will their experience:
1) Some will be convinced god(s) exist (Theist),
2) Some will be convinced god(s) don't exist (Atheist);
3) Some will conclude there is inaddequate evidence (Agnostic); and
4) Some will not show up, and not know the concept of god(s) exist (Null).
Isn't it amazing we have words describing each of these situations? Fortunately, the language is not confined to your binary approach. 2, 3, 4 are not equal.