Display Posts Query with IF function

Question

If I understand you, you want to filter out faculty members who do not have any awards at the query stage.

Replace your code:

<?php query_posts( 'post_type=mtt_page'); ?>
<?php if ( have_posts() ) while ( have_posts() ) : the_post(); ?>

with this (untested):

<?php
$args = array(
    'post_type' => 'mtt_page',
    'posts_per_page' => -1,
    'meta_query' => array(
        array(
            'key' => 'awards',
            'compare' => 'EXISTS'
        )
    )
);
$members = new WP_Query( $args );
?>
<?php if ( $members->have_posts() ) while ( $members->have_posts() ) : $members->the_post(); ?>

Note that I believe the EXISTS meta_query comparison only works in WP 3.5 onwards.

As a few people have pointed out – query_posts is best avoided.