In general the site is Google searchable. This relative anonymity protects you as long as you don't share details that can be used to id you.
There are people who archive the site not sure if partially (specific boards) or in full. It's not a great effort to be honest.
I understand the need for share with the fellow regulars whom you start considering as friends (and they are in some ways) but Tpaste is right this is a public place anyone can look at it.
Don't have to be paranoid but have to find the line to walk.
Hidden boards can be created those aren't searchable but moderation actions can give them away, and besides one might be able to find them by chance. So it's not like a walled garden tied to registration.