Can I make a search query which includes a space?

If it is possible at all, this is how it would be done:

$searchquery = new WP_Query( array(
    's' => 'hello '
));

Since all queries boil down to WP_Query at their most basic level, we can determine if it is possible using the WordPress APIs by looking at the code in wp-includes/query.php

// If a search pattern is specified, load the posts that match
if ( !empty($q['s']) ) {
    // added slashes screw with quote grouping when done early, so done later
    $q['s'] = stripslashes($q['s']);
    if ( !empty($q['sentence']) ) {
        $q['search_terms'] = array($q['s']);
    } else {
        preg_match_all("https://wordpress.stackexchange.com/".*?("|$)|((?<=[\r\n\t ",+])|^)[^\r\n\t ",+]+/', $q['s'], $matches);
        $q['search_terms'] = array_map('_search_terms_tidy', $matches[0]);
    }
    $n = !empty($q['exact']) ? '' : '%';
    $searchand = '';
    foreach( (array) $q['search_terms'] as $term ) {
        $term = esc_sql( like_escape( $term ) );
        $search .= "{$searchand}(($wpdb->posts.post_title LIKE '{$n}{$term}{$n}') OR ($wpdb->posts.post_content LIKE '{$n}{$term}{$n}'))";
        $searchand = ' AND ';
    }

    if ( !empty($search) ) {
        $search = " AND ({$search}) ";
        if ( !is_user_logged_in() )
            $search .= " AND ($wpdb->posts.post_password = '') ";
    }
}

// Allow plugins to contextually add/remove/modify the search section of the database query
$search = apply_filters_ref_array('posts_search', array( $search, &$this ) );

From this we can determine that at multiple stages the search string is stripped and cleaned, and any additional spaces would be removed as part of the sanitisation process.

The only way to conduct such a search would be to reproduce that process using the posts_search filter to reproduce the SQL using your own sanitation process, but I strong recommend against this, for security and maintenance reasons. I would advise whatever system you have, it would be easier to re-architect it than to go down this route, and it could be argued that to do so would be irresponsible as a developer, and non trivial.

Instead I suggest you do your search using a dedicated SQL tool such as workbench, and a query similar to the below:

SELECT * FROM wp_posts WHERE post_content LIKE "hello " LIMIT 0,10