Can Turnitin tell if I copied and pasted?
No
Turnitin receives a finished file. It has no view of your clipboard, your keystrokes or how the text arrived in the document.
How it works
The upload is a document, not a recording of how it was written. Pasting is invisible to it. What is visible is the statistical shape of the text you pasted.
The part people miss
Your LMS or a proctoring tool may log paste events separately. That is a different system with a different answer.
Flagged for something you wrote yourself?
There is a right order to handle it in, and editing the document first destroys your best evidence.