Yes, Turnitin will be able to detect copied and pasted texts. If you have copied a passage from another source, like an academic journal or website, Turnitin will be able to flag this.
However, whether it will be able to detect copied text from ChatGPT is still uncertain. Turnitin measures the similarity of your work with other resources out there.
Therefore, there's always a possibility of detecting AI-written text. However, this largely depends on the tone of the text produced, and its similarity to existing information.