In a perfect ideal world, questions should either be closed or answered, not both. Thus, ideally, a close-voted question should be judged in the absence of answers, since it shouldn't have any answers in the first place.
Of course, we don't actually live in that ideal world. If a question does have both close votes and answers, that can mean (e.g.) that:
- a) the close votes are bogus,
- b) the answers are bogus,
- c) the answers are correct, but the question is off-topic and should never have been asked or answered on this site, or
- d) the answers are correct and on topic, but the same question has already been asked and answered before (i.e. it's a duplicate).
Especially for close-as-duplicate votes, I find comparing the answers the question has received with those of its suggested duplicate very useful in distinguishing between options (a) and (d) above. If both questions indeed have essentially identical answers, then they're clearly duplicates; conversely, if the answers to the current question include some relevant information that is not found in the answers to the suggested duplicate, then the question should probably not be closed as a dupe after all.
Seeing the answers can also be useful for judging the validity of some other types of close votes. For example, if a question has been close-voted as "unclear what you're asking" or "insufficient information", but it does have a clear and accepted answer, then it probably should not be closed for that reason. (Of course, it might need editing to clarify it based on the given answers and comments, or it might deserve to be closed for some other reason.) The same goes e.g. for "too broad" questions that have a concise accepted answer, too.
There's an existing feature request to show answers to questions in the close review queue. The SOUP user script I've written includes a client-side implementation of this feature. I can't really speak for anyone else, but I've at least found it very helpful for reviewing close votes, particularly duplicates.