Yeah, not the way that they intended (plan was for Kellhus to either die to Aurang/The Spearman outside or be converted by the Inverse Fire), but they ultimately got what they wanted (No-God operational, no one left to interfere with their pursuit of the Absolute).
It seems they had a whole line of attempts to stop/capture/convert him. In the broader sense every attempt to stop the Ordeal was also an attempt to stop him. They tried to kill him several times over, from chasing over rooftops to nuking him. But more specifically, there's Aurang, The Spearman, Aurax+Inverse Fire, the Mutilated selling their scheme, the hundred skinspies with their Chorae and finally the succeeding agent Kelmomas to counter when Kellhus went into GODMODE. In the end, he did walk upon conditioned ground and it was not his own. Really, there could be any number of further traps ahead that we never even got to see - the Mutilated casting magic, for one. Yes, Kellhus studied the Gnosis for 20 years and they didn't, but there's 5 of them. Or how about calling up a couple of dragons?
I think they wanted Kellhus in the No-god, otherwise they could have just boxed Kelmomas the moment they captured him. I think having Kelmomas in the No-god will turn out to be a mistake in the next series, doubly so if Esmenet (his raison d'être) is still alive. I do not feel that his "two souls" ever got a reasonable use. That is, if we assume that the reason the gods could not see him was because he would become the No-god, rather than not seeing him because of his two souls. I personally prefer the no-god explanation since there must be any number of people with multiple personalities running around.
Edit: Also, thinking about it... Kellhus quite literally gave up two of his children (one fake, one real) to the non-men as part of the bargain. That could have been the Dunyadin-consult, and they could easily just have put her in the box instead. What if rather than the madhouse Insterberinth was, they had put 1-2 mutilated there. No, they absolutely wanted to try to get Kellhus in the box for some reason, even if any of his kids would do. And that reason was important enough that they were willing to risk everything.