I tested with iMessage and the other person sees it delivered, and you get nothing. When a person calls the phone rings and then goes to voicemail. It gives the person the impression that you are receiving contact and you're just ignoring them, so they think you are seeing them call or text. Instead of giving them the idea that their messages are not even coming through. It could be good or bad to block people without thinking they're blocked, so it's something to be aware of.