Is it possible to use WP_Query to only pull posts with attachments?

I am working on a plugin for generating podcast feeds, and I'm trying to figure out if it is possible to use WP_Query to pull only posts from a specified category that have audio attachments. I know I can do this in a custom query, for example:

$podeps = $wpdb-get_results(
    "SELECT SQL_CALC_FOUND_ROWS $wpdb-posts.*
        FROM $wpdb-posts,wp_term_relationships
        WHERE $wpdb-posts.ID = $wpdb-term_relationships.object_id
            AND $wpdb-term_relationships.term_taxonomy_id IN ($catid)
            AND $wpdb-posts.post_type = 'post'
            AND $wpdb-posts.post_status = 'publish'
            AND $wpdb-posts.ID IN (
                SELECT DISTINCT post_parent
                FROM $wpdb-posts
                WHERE post_parent  0
                    AND post_type = 'attachment'
                    AND post_mime_type = 'audio/mpeg'
            )
        GROUP BY $wpdb-posts.ID
        ORDER BY $wpdb-posts.post_date DESC
        LIMIT 50",
    OBJECT
);

But is there a way to do this using WP_Query? If possible, I would like to refrain from having to write the query directly, so as to ensure broadest compatiblity. Thanks!