if mform recaptcha element is included in a form it is always mandatory.
Because of this a red star should be added to it wherever the recaptcha element appears.

For instance, in moodle19/login/signup_form.php
it is written:
$mform->addElement('recaptcha', 'recaptcha_element', get_string('recaptcha', 'auth'), array('https' => $CFG->loginhttps));
$mform->setHelpButton('recaptcha_element', array('recaptcha', get_string('recaptcha', 'auth')));
but maybe it should be better:
$mform->addElement('recaptcha', 'recaptcha_element', get_string('recaptcha', 'auth'), array('https' => $CFG->loginhttps));
$mform->setHelpButton('recaptcha_element', array('recaptcha', get_string('recaptcha', 'auth')));
$mform->addRule('recaptcha_element', get_string('missing_recaptchaelement'), 'required', null, 'server');

or, better, the recaptcha element should always be provided by moodle libraries equipped with the red star, with no care for the calling function!