Hi Cody
Off the top of my head, I’m not sure S&F will work as is in the backend (it was never designed for that).
S&F runs different code depending on whether you are in wp-admin or not.
Generally speaking though, you can attach S&F to any query you create. So there might be an option for you to create your query in an ajax call (S&F should work in wp-ajax, even though its technically in admin) and you could wrap your results as a JSON object, from which you would need to parse with Javascript and take any necessary actions after that .
In order to add S&F to your query you would need to add the argument search_filter_id
.
eg:
$args = array(
'post_type' => 'post',
'search_filter_id' => 1234
);
$my_query = new WP_Query($args);
Hope that helps.
Best