This is true, as far as it goes; a family that randomly starts cueing around a deaf child is not that far different from a family that suddenly starts speaking Hungarian (to use your example) around a hearing child who doesn't speak English.
But how, then, does a hearing child gain the conceptual knowledge of what a beach and a peach are? They don't have any inherent advantage w.r.t. conceptual knowledge over a deaf child; their only advantage is that they have a tool (namely, the ability to recognize phonemes) that a deaf child does not. So, given a deaf child in the language acquisition phase, cued speech provides that tool.
Again, whether or not cued speech is the best language choice is debatable. But there is no inherent conceptual linkage - even for a hearing child - between the sound "beach" and the concept beach, or the sound "peach" and the concept peach. Language consists of a set of socialized representations of ideas, and a conceptual linkage is not required - look at all the false cognates in the world, for instance (English 'gift' versus the German 'Gift'), or the existence of constructed languages.