Depends on what you mean by a benefit. A benefit in the sense of increasing your chances of acceptance to a program? That would depend entirely on the department and the sorts of attitudes the faculty there have; but I suspect that your impression is right that Latin or Greek would probably not impress a Cognitive Scientist or Psychologist, more’s the pity 
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If, on the other hand you wonder if such knowledge would be a benefit in the sense of making you a better scholar in development or cognitive psychology with a focus on language, then I’d say the answer is an unqualified Yes – the more languages, the better!
I should have mentioned that the Harvard Linguistics Department had an interesting policy: you had to demonstrate a knowledge of all sorts of different languages: including a modern European language, one of the Classics (Latin, Greek, or Sanskrit), and at least one non-Indo-European language. I thought that was a great policy. Needless to say, the MIT linguistics department had no such requirement 
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