With settings as in https://git.archlinux.org/vhosts/wiki.archlinux.org.git/tree/LocalSettings.archlinux.org.php#n230, an https://wiki.archlinux.org user examining his Preferences/User profile/Email options is guided that
Email address is required. You can also choose to let others contact you by email through a link on your user or talk page. Your email address is not revealed when other users contact you
But when he clicks to Set an email address at that page, another page gets loaded. Within that new page, the surrounding text is
Complete this form to change your email address. If you would like to remove the association of any email address from your account, leave the new email address blank when submitting the form. Current email address: (Probably extracted from the site db) New email address: (To be filled by the user) This field should be left blank if you want to remove your email address. You will not be able to reset a forgotten password and will not receive emails from this wiki if the email address is removed.
Can the user email left blank or not? No, it can not be left blank. Probably the guidance text for allowing a blank email address field should, but currently not, conditioned on the site settings.