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I argue no, because in my experience, closed questions often (in fact VERY often) have answers that are extremely valuable.  

I have often searched for a question, found a closed duplicate, and the answers to it were more helpful for what I wanted than the answers to the original question.  

Also, I tend to think people are (more than) a little too fast to deem a question a duplicate.  At least on SE, it often happens that if two questions are about the same equation, they'll get marked as duplicates even if the question _about_ the equation is different.  Ideally such things wouldn't get marked as duplicates, but I think that's hoping for too much.  So long as they do get marked as duplicates, and get helpful answers, I don't think we should be throwing away those helpful answers for the user or anyone else who comes along later and finds these duplicates.  

Besides duplicates sometimes questions are closed because they are judged not appropriate to the community (like philosophical questions in the math community).  I often find that the people who answer these before the question is closed give extremely valuable and satisfying answers.  Again, I think it would be an unnecessary waste to throw these answers away.