Proof of concept showing how to implement virtual posts in WordPress but requires `make_post_instance` hook (or similar) to exist. See: https://core.trac.wordpress.org/ticket/12955#comment:24

virtual-posts.php

<?php
/**
 * Plugin Name: Virtual Posts
 *
 * @see https://github.com/usagov/Federal-Agency-Directory-API-Documentation
 */
class Virtual_Posts {

	const POST_TYPE = 'vp_fed_mob_apps';

	const TRANSIENT_KEY = 'vp_federal_mobile_app_ids';
	const TIMESTAMP_KEY = 'vp_timestamp';
	const DATE_FORMAT = 'Y-m-d h:i:s';

	const API_URL = 'http://apps.usa.gov/apps-gallery/api/registrations.json';

	/**
	 * @var array List of App IDs from the API.
	 */
	private static $_app_ids;

	/**
	 *
	 */
	static function on_load() {

		add_action( 'init', array( __CLASS__, '_init' ) );
		add_action( 'pre_get_posts', array( __CLASS__, '_pre_get_posts' ) );

		add_filter( 'make_post_instance', array( __CLASS__, '_make_post_instance' ) );
		add_filter( 'wp_count_posts', array( __CLASS__, '_wp_count_posts' ) );

	}

	/**
	 * Refresh the post from the API if stale by 15 minutes or longer
	 *
	 * @param object $post
	 *
	 * @return array|null|WP_Post
	 */
	static function _make_post_instance( $post ) {
		static $posts_processed = array();

		if ( ! isset( $posts_processed[ $post->ID ] ) ) {

			$posts_processed[ $post->ID ]= $post->ID;

			$timestamp = get_post_meta( $post->ID, self::TIMESTAMP_KEY, true );

			if ( ! $timestamp || $timestamp < date( self::DATE_FORMAT, strtotime( '-15 minutes' ) ) ) {

				if ( 1 <= count( $apps = self::_call_api( "Id={$post->post_name}" ) ) ) {
					self::_update_app( $post->ID, $apps[0] );
				}
				$post = get_post( $post->ID );
			}

		}
		return $post;
	}

	/**
	 * @param $counts
	 *
	 * @return mixed
	 */
	static function _wp_count_posts( $counts ) {

		$app_ids = self::_app_ids();

		$counts->publish = is_array( $app_ids ) ? count( $app_ids ) : 0;

		return $counts;

	}

	/**
	 * @param WP_Query $query
	 */
	static function _pre_get_posts( $query ) {

		if ( $query->is_main_query() && self::POST_TYPE == $query->get( 'post_type' ) ) {

			$post_ids = self::_post_ids( $query );
			$needed = array_filter( array_keys( $post_ids ), function ( $post_id ) use ( $post_ids ) {
				return 0 === $post_ids[ $post_id ];
			});
			if ( count( $needed ) ) {
				$results = self::_call_api( 'Id=' . implode( '&Id=', $needed ) );
				foreach( $results as $result ) {
					self::_maybe_add_app( $result );
				}
			}
			$query->set( 'orderby', 'ID' );
			$query->set( 'order',   'ASC' );
		}

	}


	/**
	 * @param int $post_id
	 * @return int[]
	 */
	private static function _update_app( $post_id, $app ) {

		if ( ! is_numeric( $post_id ) ) {
			$post = get_page_by_path( $post_id, OBJECT, self::POST_TYPE );
			$post_id = $post ? $post->ID : false;
		}
		if ( $post_id ) {
			wp_update_post( array(
				'ID'                => $post_id,
				'post_name'         => $app->Id,
				'post_type'         => self::POST_TYPE,
				'post_title'        => $app->Name,
				'post_status'       => 'publish',
				'post_content'      => $app->Long_Description,
				'post_excerpt'      => $app->Short_Description,
				'post_date_gmt'     => date( self::DATE_FORMAT, $app->created ),
				'post_modified_gmt' => date( self::DATE_FORMAT, $app->updated ),
			) );
			$fields = array(
				'Id',
				'Name',
				'Long_Description',
				'Short_Description',
				'created',
				'updated'
			);
			foreach ( $fields as $field_name ) {
				unset( $app->$field_name );
			}
			foreach ( (array) $app as $field_name => $value ) {
				$value = is_array( $value ) ? print_r( $value, true ) : $value;
				update_post_meta( $post_id, $field_name, $value );
			}
			update_post_meta( $post_id, self::TIMESTAMP_KEY, date( self::DATE_FORMAT, time() ) );
		}
	}

	/**
	 * @param object $app
	 */
	private static function _maybe_add_app($app) {

		$app_post = get_page_by_path( $app->Id, OBJECT, self::POST_TYPE );
		if ( ! $app_post ) {
			$post_id = wp_insert_post( array(
				'post_name' => $app->Id,
				'post_type' => self::POST_TYPE,
				'post_title' => $app->Name,
			));

			if ( $post_id ) {
				self::_update_app( $post_id, $app );
			}
		}

	}

	/**
	 * @param WP_Query $query
	 * @return int[]
	 */
	private static function _post_ids( $query ) {
		global $wpdb;

		$app_ids = self::_app_ids();
		$record_count = $query->get( 'posts_per_page' );
		$paged = $query->get('paged');
		$offset = $paged ? ( $paged - 1 ) * $record_count + 1 : 1;
		$app_ids = array_slice( $app_ids, $offset, $record_count ? $record_count : 20 );
		$app_ids_sql = implode( "','", array_map( 'sanitize_key', $app_ids ) );

		$post_ids = array();
		$sql = "SELECT ID,post_name FROM {$wpdb->posts} WHERE post_name IN ('{$app_ids_sql}');";
		if ( is_array( $results = $wpdb->get_results( $sql ) ) ) {
			foreach( $results as $result ) {
				$post_ids[ $result->post_name ] = $result->ID;
			}

		}
		/**
		 * Now add in the missing ones
		 */
		foreach( $app_ids as $app_id ) {
			if ( ! isset( $post_ids[ $app_id ] ) ) {
				$post_ids[ $app_id ] = 0;
			}
		}

		return $post_ids;
	}

	/**
	 * Load just the IDs into a transient
	 */
	static function _init() {

		register_post_type( self::POST_TYPE, array(

			'public' => true,
			'label' => __( 'Federal Mobile Apps', 'virtpost' ),
			'supports' => array(
				'title',
				'editor',
				'custom-fields',
			),
			'rewrite' => array(
				'with_front' => false,
				'slug' => 'agencies'
			),


		));
	}

	/**
	 * Load just the IDs into a transient
	 */
	private static function _app_ids() {

		if ( isset( self::$_app_ids ) ) {

			return self::$_app_ids;

		}

		self::$_app_ids = get_transient( self::TRANSIENT_KEY );

		if ( ! self::$_app_ids ) {

			if ( $results = self::_call_api( 'select=Id' ) ) {

				$app_ids = array();

				foreach( $results as $index => $app ) {

					$app_ids[] =  $app->Id;

				}

				set_transient( self::TRANSIENT_KEY, $app_ids, 15*60 ); // Cached for 15 minutes

				self::$_app_ids = $app_ids;

			}

		}

		return self::$_app_ids;
	}

	/**
	 * @param $query_vars
	 *
	 * @return object[]|null
	 */
	static function _call_api( $query_vars ) {

		$response = wp_remote_get( self::API_URL . "?{$query_vars}" );

		if ( 200 == wp_remote_retrieve_response_code( $response ) ) {

			$json = json_decode( wp_remote_retrieve_body( $response ) );

			if ( is_array( $json->results ) ) {

				$results = array();

				foreach( $json->results as $index => $object ) {

					$results[ $index ] = $object;

				}

				return $results;

			}

		}

		return null;

	}

}
Virtual_Posts::on_load();