Not really. We’ve had forums that literally allow you to post to them without even signing up with an account. Without being a “user” at all. This isn’t about “checking” anyone, it’s simply about limiting its ability to be used as a troll tool below the point at which it becomes too tedious to bother. At that point you have eliminated 99% of it.
This CSAM poster is 1 single person among hundreds of thousands. Making it too tedious to perform eliminates them along with the problem entirely.
I worked at the server company that previously hosted discord servers (no longer exists) and let me tell you right now that all your conversations were accessible on the server to anyone in the company and completely and totally insecure. Overall security was pretty meh and it wouldn’t be very difficult for anyone who really wanted the information to gain access to anything on your server.
It is not a valid place to store or discuss anything that requires operational security. It is also not a place where customer data should be stored or discussed, in fact you’re also probably breaking gdpr by accident if you ever do so.