Not OP, but you can influence how deterministic your LLM behaves using the temperature setting. The neural network doesn't directly output tokens, but logits which are then converted to probabilities and then a token is chosen at random, unless the temperature is 0 (i.e. greedy, we just always pick the most probable token without any randomness). All speculative decoding methods have to "commit" to a token though even when they don't know the actual logits of the full size NN yet. The question then is (and I don't know the answer): how do the common inference engines behave when the speculation landed on the most probable token, but the random choice still doesn't land on it? You can imagine that in the interest of performance as long as we stay reasonably inside the probability we just go ahead with the speculation. Not sure if thats implemented like that though.

Edit: I just looked up the math, and actually the idea of speculative decoding is done in a clever way that fully preserves the probability distribution while still maximizing the acceptance rate of draft tokens. So I would have to disagree with OP and say that no, non-greedy sampling doesn't influence the trajectories.