ADHD is in no way an indicator of intellectual ability, and there are many gifted children who also struggle with attention deficit disorders. This is referred to as twice-exceptional (2e) -- when a child is gifted and also has a disorder or disability such as ADHD or learning disabilities. However, it's important to remember that the two (ADHD and giftedness) are not linked and there has never been any evidence that shows ADHD is a symptom of being gifted, as some people mistakenly believe.
Unfortunately, in many cases a child's ADHD may prevent him from being identified as gifted, since symptoms (inattentiveness, impulsiveness, and hyperactivity) often negatively affect the test scores that schools rely on to tell if a child is exceptional. What's more, teachers are often so focused on managing the disruptive behaviors associated with ADHD that they fail to pick up on signs that a child is gifted.
On the flip side, problems also arise when school counselors, psychologists, psychiatrists, and pediatricians misdiagnose gifted children as having ADHD, as a result of not truly understanding the characteristics of being gifted. For example, most gifted children have a much higher activity level than their peers, but this need for stimulation is often mistaken for hyperactivity. Gifted children also tend to be impatient and uninterested in school -- not because they can't focus, but because they're simply bored and frustrated.