Probably not the AI personality. AI personality is determined by ethos and race traits, and as it turns out nerve stapling is a racial trait.
Not quite. There is ample Precedent for a Race Trait being a requirement or positive weight to pick a certain AI personality:
Only a decadent species can become Slaving Despots or Decadent Heirarchy.
Only conformsits can become the Hive Mind AI type
Only Normadic or Breeder can become Migratory Flocks.
And last but not least, Metalheads and Fanatic Befrienders have 2 and 3 Trait requirements respectively.
The new Hivemind AI type can actually check on Ethos, Government Form and Racial Trait to figure out that they should be a hive mind.
One of the new traits unlocked via Biological Ascension is "Nerve Stapled", which removes a species' ability to feel happiness or sadness. If you created a new empire (via vassalization or liberation wars) with these guys as the primary species, would it affect their AI personality?
I would guess the same that happens if you liberate a mostly T2 Robot Empire.
I doubt Neve Stapeled pops will be considered "sentient" for the purpose of being the Primary species of a new Empire. If there is any non-Nerve-Stapeled species among them, they would propably become the primary species.
If there is absolutely no eligible species: Well, there is a case where rebelling slaves join a rivaling empire.
It could be that the invalid Empire just spontanously decides to "join thier liberator like a conquest", because they lack viability on thier own.