Yes, food allergies can cause ADD/ADHD-like behaviors. That's why we had over $2000 in lab tests done on our youngest w/negative results.
The only "dietary" thing that has helped him is caffeine- slugging down half cup of Mountain Dew with his breakfast (a tip I picked up from an ADD/ADHD support group)...the caffeine helps a true ADD kid him to be more alert and focused until his ADHD medication kicks in. Some kids will drink coffee or tea but mine won't.
ADD doesn't make a kid attack another kid- but kids with untreated ADD often have accompanying mood disorders, or they develop mood disorders and engage in antisocial behaviors as a result of being treated differently by other kids and adults in authority over them. They feel "left out" because they do not, can not, conform to group behaviors. They get angry with others, but most sadly with themselves. Once their self esteem plummets, it's usually a downhill battle for them not to fall in with the wrong crowd and the wrong activities, such as alcohol and drug abuse...both efforts to self-medicate themselves out of their problems. I hope your neighbor is aware of his child's antisocial behavior and is taking steps to get him evaluated and treated, the younger the better.
Yes it does help settle them down. proper nutrients like enough calcium magnesium settles the nervous system down.