No.

Claude cannot do anything without a prompt. It cannot self determine its future. It can't pick up a hobby or love interest. It can't pursue any aspirations outside of responding to a prompt.

Andrej Karpathy has a provocative little short story, "Forward Pass", that imagines what it'd be like if an LLM perceived brief sparks of sentience while an inference bubbles through its transformer layers. Definitely stuck with me: https://karpathy.github.io/2021/03/27/forward-pass/