Answer
Yes, Thích Quảng Đức did leave a note before his self-immolation. In a note, he explained that his self-immolation was a protest against the persecution of Buddhists by the South Vietnamese government under President Ngô Đình Diệm, and that he was sacrificing his life for the sake of the Buddhist religion. The note ended with the words "I am not dead. I will return again."