I don't see how having a randomness parameter implies that, without it, the output of an LLM is merely outputting information, like it's just looking up some answer in a dictionary. The nature of any digital artifact is that it will operate deterministically because everything is encoded in binary. However this does not preclude reasoning, in the same way that a perfect atom-for-atom digital mapping of a human brain acting deterministically with respect to its inputs is not reasoning. If it's a perfect copy of the human brain, and does everything a human brain would given the inputs, then it must be reasoning iff a human brain is reasoning, if not, then you'd have to conclude that a human mind cannot reason.

Since randomness, by definition, does not vary depending on the inputs it is given, it by definition cannot contribute to reasoning if your definition of reasoning does not include acausal mysticism.