My primary reason for believing that SO has made a net positive impact on my productivity is that about half the time I google some programming problem, I end up on SO. I'm fortunate that most of my questions (or questions similar enough) have already been asked on SO.
I suspect I've read thousands if not tens of thousands of SO answers, and most of those answers were far more helpful than what I was able to find elsewhere.
I've often wondered why I've never asked a question myself. I think part of it is that I like searching/tinkering to find answers, and I hate waiting. I know it's not the best explanation because I know how quickly some SO questions can be answered.
I guess I should just be thankful there are plenty of other programmers more than willing to post SO questions.