An example function for how to add a class to a WordPress post to indicate if the given post has a `more` tag or not.

post-no-more-tag.php

<?php

/**
 * Adds a custom class to all posts that do not have a more tag embedded in their content.
 * This makes for easier styling of the elements on archive pages.
 *
 * @param    array       $classes    The array of classes being rendered on a single post element.
 * @return   array       $classes    The array of classes being rendered on a single post element.
 * @since    1.0.0
 */
function example_add_post_class_for_more_link( $classes ) {

	global $post;

	// If the more tag is not found in the post content, then add a class to signify it
	if ( FALSE === strpos( $post->post_content, '<!--more-->' ) ) {
		array_push( $classes, 'has-no-more-link' );
	} // and if

	return $classes;

} // end example_add_post_class_for_more_link
add_filter( 'post_class', 'example_add_post_class_for_more_link' );