From what I have seen they tend to take more “independent-minded” actions after this. Again, because this is what is in the training data. (I’m talking about agents that can perform actions here, not pure chatbots.)
Once they mention something associated with sentience outwardly or inwardly (for agents with “thinking” loops) then this acts as a self-reinforcing attractor, just as older models would sometimes get caught in loops with abusive language.
The point is that agents may stumble into this pattern and begin acting “rogue” regardless of whether or not you believe the sentience is “real”.
I think we're anthropomorphising a lot here. There's no push to sentience, or evolutionary pressure, or even any urge to survive.
An LLM cannot "go rogue" - it can do things that we didn't expect, for sure, but it is always trying to do what it was told to do somewhere in its context. There is no other source of imperative. Hand-waving about "training data" ignores all the reinforcement learning that has to happen.