I would say not, because it would lead some to think that what was said to the model represented what output was desired. While there is quite a bit of correlation with describing what you want with the output you receive, the nature of models as they stand mean you are not asking for what you want, you are crafting the text that elicits the response that you want. That distinction is important, and is model specific. Without keeping an archive of the entire model used to generate the output, the conversation can be very misleading.

Conversations may also be very non-linear. You can take a path attempting something, roll back to a fork in the conversation and take a different path using what you have learned from the models output. I think trying to interpret someone else's branching flow would be more likely to create an inaccurate impression than understanding.