No, the account is banned so it can’t be ‘active’, at least not in the traditional sense. Mod-only activity lists show his last login was over two years ago.
He can delete your wall posts and edit his profile because banned users do have those abilities. If what you’ve mentioned is accurate, I don’t know why he is still checking this website. He can’t do anything outwardly. Maybe he has email notifications on.
What’s with everyone’s fascination with this guy? He’s just some dude from three years ago who got banned. This account was peak-2013.