My guess is no because it comes across as pushy/desperate (and in my case, it is). I've never done this. I'm not asking for WHY they didn't hire me. The answer for that is most often they found a candidate who was a better fit for the position.
I want to ask what would it take for a candidate to be hired, what experiences I should have, what specific skills and/or experience are required that I may not have come across during my research, etc. To a degree, I think this is proactive, but my hunch says don't do it.
I have asked these questions on that dreaded phone call when they told me they hired someone else, and they are often speechless or reluctant to share information... but I need to know. Maybe I shouldn't have, let alone contact them myself.