This isn't a terrible idea, we would just need to make sure folks don't just go out half-cocked and start writing every single question that comes out of the discussion. One thing we've all learned is that hypothetical or "fake" questions tend to sound like what they are, fake or manufactured, and it takes a special skill set to write a question so that it does sound like there's a real, actual problem to be solved.
If managed properly, this could help us better define our scope, or identify real, actual problems we've observed our colleagues face that we could ask on their behalf.
The Water Cooler chat room has scheduling features built in to where we can schedule an actual event in the chat room and advertise it in the bulletin board on the main Q&A page.
If there is interest in this, and a plan for making people aware of what the goals are, we can make arrangements to schedule something. But it's critical that everyone involved believes that quality trumps quantity.
I'd suggest doing this in two scheduled phases. In the first meeting, you simply identify some possible questions, but don't ask them on the Q&A part of the site, not yet. We don't want to flood the site with questions that aren't going to work out as this might just make people feel bad who are really trying to help. Then, before the second meeting, pick a few of the best questions and work together to ask them and edit them as a group so they're outstanding posts. We might also consider whether these should be community owned posts, meaning anyone can edit them and no one single person gains all the reputation.
Of course, at the end of the first meeting, you might just decide that, hey, this really is a bad idea and none of these questions will work. In that case, there's no harm done. Conducting this experiment in a controlled manner will likely yield better results than visiting the site one morning and finding it flooded with downvoted, closed questions. :)