It (at least LLMs) can reproduce similar display of having these emotions, when instructed so, but if it matters or not depends on the context of that display and why the question is asked in the first place.

For example, if i ask an LLM to tell me the syntax of the TextOut function, it gives me the Win32 syntax and i clarify that i meant the TextOut function from Delphi before it gives me the proper result, while i know i'm essentially participating in a turn-based game of filling a chat transcript between a "user" (with my input) and an "assistant" (the chat transcript segments the LLM fills in), it doesn't really matter for the purposes of finding out the syntax of the TextOut function.

However if the purpose was to make sure the LLM understands my correction and is able to reference it in the future (ignoring external tools assisting the process as those are not part of the LLM - and do not work reliably anyway) then the difference between what the LLM displays and what is an inherent attribute of it does matter.

In fact, knowing the difference can help take better advantage of the LLM: in some inference UIs you can edit the entire chat transcript and when finding mistakes, you can edit them in place including both your requests and the LLM's response as if the LLM did not do any mistakes instead of trying to correct it as part of the transcript itself, thus avoiding the scenario where the LLM "roleplays" as an assistant that does mistakes you end up correcting.