Yes, Ajokli was "short-circuited" by the proximity to the No-God in the form of Kelmomas. When Ajokli-Cnaiur walked into the Whirlwind, the same thing should have happened the moment he came into the No-God's direct area of influence. If he didn't, then just the body was destroyed (by the Whirlwind, without getting directly influenced by the No-God), and Ajokli can hop between them even when forced out, like he hopped from Kellhus to Cnaiur.
Just why Ajokli stopped inhabiting Kellhus isn't clear to me; it seemed like he was shocked at being approached by something he did not see coming (though whether it was Kellhus who was shocked or Ajokli, that wasn't really clear either).
However, Cnaiür comes far more closer to No-God. This is the book section:
The Whirlwind blotted all Creation before him, blowing bodies outward and sucking bodies up as it advanced. A million blasting needles sheared the scars from his skin, leaving his windward surfaces striped in living fire. And they roiled like burning grease within him, the indignities he had suffered, the grudges and grievances he bore! Such a toll as only murder could redeem!
“SHOW THYSELF SO THAT I MIGHT STRIKE THEE!”
Skin pealed back from tissue, sloughed as parchment. Bleeding was struck into mist.
WHAT DO YOU SEE?
Even as it blinded the wind laid bare, exposing structures, devouring them, displaying the lurid layers beneath. With Hell’s own eyes, Cnaiür urs Skiötha peered up into the void and saw … nothing.
“REVEAL! REVEAL THYSELF!”
Flesh disintegrated. A vicious black climbed over all things, grew numb.
WHAT AM I?
"With hell's own eyes", he looks at No-God, and sees nothing... which is in keeping with the idea that the Gods can't see him. But unless Ajokli is the runt of the litter, the god of stupidity or the intellect of gods work in different ways, he should be able to realize something is up with the No-God.
Assuming he didn't die, of course. Unlike Kellhus's death, there is no indication that he actually left Cnaiür at this point. But that's a rather useless argument, because Bakker's prose was frustratingly vague towards the end of this book.
At some point I speculated that the host influences Ajokli's personality, so Ajokli-Kellhus is not completely the same as Ajokli-Cnaiur. The nature and goals of the Trickster are preserved, but some quirks of the host's personality also play a part. Like, for example, Kellhus's scheming or Cnaiur's hatred. Other people went even farther, postulating that it was the "birth" of Ajokli the Trikster and at the same time Prince of Hate as he described in the books. It invokes atemporality in exactly the same way you did below.
That's a bit anti-climactic, isn't it, that a God should insert himself into the story in like, two chapters of the book, and be born through it? I'm more inclined to believe that Ajokli is better disposed towards connecting to Kellhus and Cnaiür because his realm is deception and hatred, than being born out of them. Though he could perhaps be an amalgation of the two, I don't find it likely that he gained his definining attributes through a few minutes of contact to two mortals (if they are, at all!)
It's really hard to speculate about the God of Gods, since Bakker expressed very strange views on the subject through Kellhus (his talks with Proyas). I'm completely unsure whether the concept of causality, for example, is at all relevant when we're talking about the God of Gods.
Well, we can discern a few things. Both Kellhus and Koringhus, possessing probably the two greatest intellects in the series, grasp the nature of the God of Gods through distinct means, and their understanding of it seems to match each other. Both of them, for example, point out that the idea it has human features (as in, emotions), is faulty.