No, that's not at all how it works.

"Hellbanning" is a form of banning where the site takes steps to avoid tipping you off that you've been banned. It's ostensibly a defense against spammers and trolls, who will create new accounts after being banned.

For the past couple years, bans on HN are announced publicly. They're not automatic; the moderators do it directly. It's not based on your karma.