I often see a question that is a duplicate, but the question is well-stated and good in general.
So I ask: is it correct/encouraged/frowned-upon/... to up-vote a question at the same time you vote for closure as a duplicate?
I frequently do this. The two decisions are almost completely independent for me. The only time that the presence of the duplicate would mean that I didn't vote would be if the original question was blatantly easy to find (something like the "How do I look up a symbol?"). If someone's put some effort into their question, they probably did a cursory search of the site and didn't find the original. I know how hard it can be to find questions here - even my own questions/answers that I know exist! - so I'm generally very lenient on others not doing so.
Lastly, if it is a duplicate - and with the exception of classics like "How do I look up a symbol" - the implication is that it is on-topic for the site and a question that is worth having, just that we had it before. So if I see it's been voted as a duplicate, my bayesian prior is already weighted to the upward vote.
I have simultaneously upvoted and voted to close questions on a few occasions, but I only did so when the duplicate question was either exceptionally well-stated or when it turned out that the matching original question was hard to discover, usually because of improper tags.