I like the idea. Like CV said, SO does it quite nicely and it works well.
Sure, I agree with you, but it's better than nothing. If I came from Google it would help me greatly if I could go to the most popular post/answer because the majority of the time it's going to be the best solution. If not, oh well, you're back to where you were before.
I think there are too many posts for that. It would be a bit chaotic.
Too complex. Just keep it simple. You have a question, vote what's the best all around answer. Like I said above, people searching for a question are benefited best from a simple 'this reply is the most popular answer'.