I would maybe wait 2 weeks, but with no word/contact at all, I feel like that's generous.

In a perfect word, sites that required an interest application of sorts to join would inform you if you've been denied instead of just letting you wonder. That being said, if I was waiting a month for a reply and saw the site was advertising and that they were not closed; I wouldn't want to join. I can't imagine setting your site up and not having a system in place to review the interest summaries.  Sure, some things can fall off your radar, but that would just be a signal that the sites probably not it for me.