How to make WP register page as search when query is ajaxed

I've created a search page using an archive page and a JS ajax script to pull in results from a custom wp_query(). The problem I'm facing is that WordPress doesn't register this page as a search page (is_search() returns false).

I'm guessing the is_search() checks the main query, and this doesn't register since it's a custom query?

How can I make WP register this as a search?

I've included the code I'm using. Shortened to only the relevant for brevity.

Javascript

// Get Search Form Values
function getSearchValue()
{
    var searchValue = $('#rfp_search').val(); //Get search form text input value
    return searchValue;
}

function run_search(paged){
    var ajax_url = ajax_search_params.ajax_url;

    $.ajax({
        type: 'GET',
        url: ajax_url,
        data: {
            action: 'get_search',
            search: getSearchValue()
        },
        success: function(data)
        {
            $('#search-results').html(data);
        },
        error: function()
        {
            $("#search-results").html('<p>There has been an error</p>');
        }
    });
}

archive-rfp.php

<div id="search-results"></div>

functions.php

wp_register_script( 'ajax-search-js', get_stylesheet_directory_uri() . '/library/build/js/ajax-search.js', array( 'jquery' ), '', true );
wp_localize_script( 'ajax-search-js', 'ajax_search_params', array( 'ajax_url' => admin_url( 'admin-ajax.php' ) ) );
wp_enqueue_script( 'ajax-search-js' );

add_action ('wp_ajax_get_search', 'om_ajax_search');
add_action ('wp_ajax_nopriv_get_search', 'om_ajax_search');

function om_ajax_search(){

    $query_data = $_GET;
    $search_value = ($query_data['search']) ? $query_data['search'] : false;

    var_dump(is_search());
    var_dump($tax_query);
    $args = array(
        's' => $search_value,
        'post_type' => 'rfp'
    );
    $loop = new WP_Query($args);

    if( $loop->have_posts() ): ?> 
    <p><?php global $wp_query; echo $wp_query->found_posts.' results found.'; ?></p>
    <?php 
    while( $loop->have_posts() ): $loop->the_post(); ?>
        <h5><a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></h5>
    <?php endwhile;
    else:
        echo '<h2>No Posts Found<h2>';
    endif;
    wp_reset_postdata();
    die();