I would expect any pre-prompt or fine tuning training that is relevant to the subsequent prompts to improve the results (relative to the pre-prompting or tuning

I would expect any pre-prompt or fine tuning training that is relevant to the subsequent prompts to improve the results (relative to the pre-prompting or tuning). Likewise, any pre-prompt or fine tuning training that is NOT relevant to the subsequent prompts adds unhelpful and highly non-contextual complexity to the models job, so likely to reduce the quality of response.