I think that really depends on the starting prompt you give a LLM. Did you read the GPT 4 paper from OpenAI? When tasked with solving a captcha and allowed access to TaskRabbit it tasked a human with solving the captcha. When the human jokingly asked if it was in fact a robot, it reasoned that it should lie to the human about that and then made up a convincing sounding lie.
I don't think a paperclip style AI is too far fetched.