Is it possible to determine whether a page is a page template by page_id in ajax call?

To get the page template of an arbitrary page by ID you can use get_page_template_slug():

// Set $page_id somehow, probably getting it from AJAX request.

$template = get_page_template_slug( $page_id );

if ( $template === 'templates/about.php' ) {
    // Do something.
}