While he is physically an adult, if he has the capacity of a 7 year old, and children aren't invited, then he shouldn't be either. If his parents will not attend without him, then that is their choice.
If children are invited, then maybe someone close to the parents could suggest they keep him more under control, although I'm sure no one wants to go that route.
I know a family that has a Downs child who is an adult, and likes to hug (especially women). His parents keep him under control though and tell him when it is enough. He listens very well and I would have no problem inviting him, as long as his parents were there too.