One encourages better quality questions, the other helps a person with a problem. Both admirable goals. Right?
What is meta?
- Any Stack Exchange user can ask a question
- The community provides support, votes on ideas, and reports bugs
- Your voice helps shape the way Stack Exchange operates
Most certainly not. This is the reason there is an independent score for the question and each answer. A terrible, un-researched, l337 sp33kin' question could be downvoted to oblivion and still attract a fantastic answer. There's even a badge for extreme cases.
Remember that votes are not permanent and can be removed if the post was edited since the vote was cast. I use downvotes sometimes (along side a comment) to encourage the user to improve their question. Once they have done that, I'm very happy to remove and possibly even reverse my vote. Till then, if I can help the OP out by providing an answer there is no reason not to.
There is only one thing that's a bit concerning, answering a sub par question gives it a (mostly false) sense of legitimacy1 (assuming of course the answer is good). If the question is truly crap, I would probably not answer it and go for the downvote / close vote combo.
If, on the other hand, the question isn't that bad, but still worthy of a downvote, I'd say go for it. It would be nice if you also spend some time helping the OP fix the question (commenting / editing), and awesome if you retracted your downvote if they actually fix it, but you've already done enough by answering the question, it's completely up to you to decide if you'll go the extra step or not.
1 The "Eeek! How can it be not a real question when someone answered it!" phenomenon.
I would say it is the opposite of unethical! (very ethical?)
Just because you don't think it is a good question or there are issues with it does not mean you can't provide an answer. I think it is very honest to do this.