Nice Idea... wish every area did this... might I suggest using Discord instead of Slack? Discord is more obviously for "gaming", slack works perfectly well but slightly more usually oriented to "getting work done" I'd say.
edit: Evan, mostly so others emulate something that works... I'm not sure why bother with private-invite style, just post URL right?
I don't know too much about Discord. Seems pretty silo'd into video gaming. There are actually a fair number of club/hobby Slacks out there. I picked Slack cause it's flexible and lots of people already use it for work or other hobbies (Ingress, etc). Having multiple Slack rooms open is really easy to navigate. So for the folks who already use it for work it's an easy sell.
Right now, it's just off of the ground, so it's invite only. All users do have invite privileges though. I will be working on a landing page to automate invites in the near future.