Well, I don't think anyone really knows how the No-God works, except maybe the Progenitors themselves. Or, much like some of our neural-networks now, we actually don't know exactly what they do, only that it gets done. So, the Sarcophagus might just be a literal block-box, that just does what it does. It might even not have been made by the Progenitors themselves. If it was the case that Ark was an AI or something like that, it might have devised the Sarcophagus itself with little to no understanding of any deeper meaning. So, indeed, almost anything is likely potentially "on the table" because there is so much undefined.
As for what happens when the No-God is destroyed, well, we don't know. However, since the Consult didn't just suicide themselves when the No-God came to be the first time means, either, the souls get set to the Outside, or stuck in a transitory state, or something "worse." In any case, part of the Consult plan is to specifically "close the world" and then enjoy corporeal life. So, it could be that souls under the No-God just cease to be but the Consult is averse to this outcome. They are after life, eternal, not an existence of damnation or simple non-existence.
Not only that, but part of the scheme is to end the system. That is, to close of damnation altogether. In this sense, they do have a "noble" aim, even though it's actually terrible, just in a different way than the Cubit's demands are.