Actually, that bit of line is my personal own flavor, sorry it doesn't sit well with you
Rather than say it doesn't exist in reality, I suppose I should have used the more common phrase of
'Does not yet exist in this world or Universe', take for example his weapon the [Blasting Rod], when he summoned it because it was made from materials not of this reality, it could not manifest properly. Indeed, we don't know the constrains of his power, similar to the other broken characters from before, we'll eventually be told of some loophole.
Actually, Aleister's been slowly achieving his plans since the start of the story, it's just wasn't as obvious as the other villains. Building Academy City, The cloning of Mikoto, spreading them around the world, the creation of an artificial 'Heaven' and Angel, writing the book of the law. All in all it's his first plan of making magic obsolete, where he intends to go from there is anyone's guess.
And I never said it was beyond human understanding, I said you cannot used Christianity to explain it or rather you cannot look at it through only that point of view because Crowley is trying to use science to perform magic... I think there was something being said about that when the real-life Crowley created his religion of Thelema but that's another bunch of stuff I don't fully understand.
One can't really mention an Angel without thinking of the Christian version. Indeed, the mere mention of Angel (and even the images of Aiwass) brings out the visual of a beautiful entity swathed in light, wings, halo, etc. Even if we increasingly become unable to use Christianity to explain things, we are still using Christianity and elements from its folder. At the same time, the very fact that we need other forms of religion or cultures to explain only underline the fact that things may not be as they seem. There is too much "beyond" or "out of our understanding," of which are elements of Lovecraft mythos.
In any case, looks like the halo and wings are going to stay for most parts
The explaination of Aiwass' existence seems to fall under one of those
Secret Chief, there a wiki site for you. Long story short, The Secret Chiefs are said to be transcendent cosmic authorities, a Spiritual Hierarchy responsible for the operation and moral calibre of the cosmos.