From a practical standpoint, yes - that is the intended meaning of the sentence. From a literal standpoint, no, "prepare" is a distinct verb in Italian with the same meaning as it has in English. From an aesthetic standpoint, "The cook cooks the food" is an awful sentence in English, and I would hazard that it's not much better in Italian. The sentence to translate should probably be "Il cuoco prepara il cibo."
As an aside, both my physical and online dictionary list "To - dinner" as the first entry, which suggests this is one of the most common use of the Italian verb "prepare".