After I setup my lemmy instance a few weeks ago and subscribed to a bunch of communities, I played around with the options to see what they do. I toggled the private instance to see what happen. Turns out it can federating just fine. I could post and comment in the communities I subscribed. Then I realized there are two big problems with turning on the private instance option:

1. I checked the mod logs on some large instance, and turns out they are banning private instances that they came across with (possibly those private instance were a source of spam accounts). Luckily my instance is not banned.
2. When I restarted my lemmy container, it refused to run again, throwing error about how you can’t turn on private instance option and federation option at the same time (even though it’s working when I tested it). I had to toggle the private instance option off manually in postgres table in order to get lemmy start running again.