Why is it that we're going with the most literal possible interpretation of the "nowhere" part of the major's statements, while being forced to take the "everywhere" parts as meaning "anywhere", an entirely different word which in this case means something entirely different from the literal interpretation of "everywhere"? The two words are said in the same breath seperated only by the word "and", and yet we're trying to take one as meaning a different word entirely while taking the other as meaning a very literal and very specific application of that word.
Let's go through the major's statements. We'll proceed with the assumption that the words are literal and not hyperbole like the word used to describe literally the other half of Schrodinger's state.
Major said the following.
"he is nowhere"
I said above that in a sense you could argue a disembodied soul with no ability to manifest or interact with anything could be referred to as being nowhere. It has no body, and can't affect the world at all or appear even as a powerless observer. Where is it? In a sense I'd say it's nowhere, even by definition, since it isn't anywhere.
"imaginary numbers"
I guess it means imaginary information. First of all it seemingly refers to his ability to imagine himself and perceive himself how he wants to, unless we want to ask if it's someone else's imagination which doesn't make much sense, or we can treat the presence of an observing imagination as not being literal. Not a bad trick, that's where his low godly comes from. But what is he observing/imagining, and what with? Can he observe his own soul and decide if it exists, something which would be used to say mid-godly as it would require him to exist beyond that soul as some kind of higher concept or higher dimensional existence? Or does it extend only to his physical form while the observer is Alucard's disembodied soul? A disembodied soul still might be able to harm itself and kill the other souls attached to it or inside it, so the soul being non-existent is still hard to be sure of.
"(Schrodinger's) existence itself is equivocal"
The issue is, define existence, specifically the way the major intended it, keeping in mind that the major had already used hyperbole for the "everywhere" part. Wouldn't something that can literally imagine itself anywhere in the world and in whatever state of health it wants and then have that imagination become reality, all while its body will vanish if it can't recognise itself have an "equivocal" existence, open to interpretation? That already makes its existence in the world entirely open and subject to its own interpretation, which fits the major's words rather well, in fact, if its existence is entirely subject to its own interpretation that fits the description quite literally of an existence open to interpretation. As for his existence vanishing, does a dead thing that has no physical trace of it remaining still exist? By some definitions and belief systems no and by some yes. The term non-existence in regards to versus debating is intentionally more specific than the way most people use the word.
Look, I like the idea of Alucard being an unbreakable wall too. It's just that when abilities are given and taken by things like this, especially when the ability is such a huge deal for the character's performance, the statement being open to other interpretations and being in a description filled with other statements that are hyperbole or less than literal in any way is an issue. I guess I can get behind Schrodinger being able to render his body non-existent, in a non combat-applicable sense, and only in the sense that his body is like a projection, but extending it to his soul just seems unsubstantiated when souls are generally immaterial.
TL;DR: Schrodinger is stated to be everywhere and nowhere (the "everywhere" part is already treated as hyperbole due to anti-feats, so the major's statements are already less than 100% factual) and stated to have an existence that is open to interpretation. These statements are both covered by the fact that he can imagine himself in any location, and without any damage, and it will happen. Non-existent physiology could follow, but isn't certain.
He is also stated to be imaginary information, but this statement is only after being rendered unable to manifest, removing the "everywhere" part of the above statements. These statements do imply, at least somewhat, the erasure of his body, but don't really apply to his soul. Souls in Hellsing are never shown in any material form, nor is their nature ever described. We know his body disappeared, but his soul is never proven to have been erased, only disembodied. If his body was erased and his soul disembodied he would still be able to destroy his other souls that are attached to his own and the statements would still fit.
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