Well, actually I think it all depends on the child. Sometimes food allergies are the consequence of the child's hyperactivity and parents may think is ADHD when in fact is a nutrional problem. I do not know with other parents but with my son no matter what he eats (whether contains sugar or not) he is always hyper. We tried in the past to cut all sugar products and others but he continued behaving in the same way. I think is extremely important good nutrition in a child (whether he has or not ADHD).
I was talking to a mother of a child with ADHD the other day, and she had been told by the hospital that her Son should start going on a casein, wheat and gluten free diet, as the Dr and other medical people were inclined to think that these ingredients were causing some of the hyper activity in her son.
Since starting on keeping away from these ingredients, she said that she has seen a significant improvement in her son. I don't think this is a cure, but I think it may help improve the condition, so it may be worth trying this if your child has ADHD.