ADD 4 year old?

Hello! I'm looking for advice/opinions/experience from anyone and everyone who knows anything about ADD/ADHD. I nanny for a family with a (almost) 4 year old boy and an 18 month old boy. The parents don't believe in discipline whatsoever. They don't believe in time outs or consequences. They basically just let the children do WHATEVER they want. It's extremely difficult for me to handle the children. That being said, the 4 year old little boy is extremely annoying. I don't know how else to say it. I've always just thought this is a product of his lack of discipline and structure from his parents. However, I recently came accross and article about ADD and each and every symptom sounded like him. 
He's constantly singing/yelling/making noise, even when he's alone in his room. He's extremely loud. He's always running around pretending to be different trucks/animals. He never listens to directions. You can tell him to stop 100 times and he'll just do it again. He doesn't listen to directions AT ALL. He's very irritable and easily gets upset and screams. It's impossible to have a conversation when he's around. He's always interrupting and yelling for attention. He doesn't understand personal space with his brother or other children at school. He's always touching/squeezing/hugging them. When they tell him to stop or get upset, he just continues doing it. Does anyone have an opinions as to whether this is just misbehavior or something actually medical? 

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