It would be more representative, but the thing that would kill it is it would also be annoying. I rolled my eyes at reddit pushing non-subbed content to me, and it would personally feel like a callback to that. Not out of disinterest in the poll, but because I didn't get to choose. User-generated pop-up is still a pop-up.
I'd be concerned about the possibility it may end up being a sub that's popularly blocked to avoid being spammed with unwanted questions, or at least one that's complained about.