Unlikely to occur. Beehaw's admins hate dissent and anyone questioning them. Well before the blackout, they literally had a "no sources" rule because users kept questioning the mods. Likewise their current "rule set" states what they say, goes, and that everything is up to them, not the rules. They say that with all cases (except obvious trolls), that they will always warn first. I have yet to ever see any kind of warning from any of their admins.
They were being questioned on sh.it and on lemmy.world, so they blocked both. You can check their modlog to see just how little spam they had to deal with.
You can also pop in to look at their discord to see how much they dislike the criticism.
I read the "essays" the beehive have to "join" and take part. In my view they wanted to make a space for their own community and choose a fediverse where they should have picked a closed off forum/discord/redditcopy.