In our experience, it worked very well.
Once our boys had been on the diet for a couple of weeks the violent temper tantrums had gone from several every day, usually for no discernible reason, to about one or less a week, always with an obvious cause. That result certainly made it worth eliminating artificial coloring and flavoring from the family diet, but we found letting the kids eat sugar had no effect on their behavior at all.
Some people say the Feingold diet only works for psychosomatic reasons, but there were times when nobody knew the kids had gotten a trace of something forbidden and they reacted anyway. I remember one time the ingredients in a certain kind of cereal had been changed, but the company continued using up boxes with the old ingredient list on them. Not only our kids, but those of several other people in a support group we belonged started showing their old behavior problems within a few days of each other. None of the parents could figure out what was causing the problem. Sure enough, all those kids had eaten the cereal with the new ingredient and as soon as they stopped eating it their behavior improved again.
The hardest part of following the diet was avoiding fruits and vegetables high in salicylates, and I've since learned that in other parts of the world different produce is on the list of foods high in those chemicals. That may depend on differences in the soil. It's impossible to eliminate those natural chemicals completely, but avoiding them as much as possible does make a difference.
However, if even a trace of artificial coloring or flavor, such as in medication, is ingested it will cause a reaction so there's no point in just cutting down on those things.
The Feingold diet may not work for every child with ADHD, and I've heard it seldom helps adults, but it's certainly worth trying.