Can a gifted child have adhd?

Yes. Yes, there are many examples of highly talented and successful adults who have adhd--some began as "gifted" children in some areas. It is a disability that requires extra efforts, but it does not necessarily result in disappointing outcomes or unsatisfying lives over the long term.
Dr. Smith speaks the. Truth. Multimodal treatment (behavioral therapy, environmental manipulations & medication management) are vital for academically gifted children with adhd to reach their potential. They benefit from a "section 504" in school for test accommodations. Many start learning how to structure their environment for optimal learning & academic output by age 10. See chadd.Org.