Is there a way to conditionally check whether a WordPress post title is empty?

While you’re in The Loop you can check against the WP_Post Object like so:

<?php while( have_posts() ) : the_post(); ?>

    <?php if( ! empty( $post->post_title ) ) : ?>

        <h1><?php the_title(); ?></h1>

    <?php endif; ?>

<?php endwhile; ?>