I came across this snippet that adds a coupon to the order mail.
  I would like to make it appear in the processing order mail only if the customer have not used any coupon.
  add_action( 'woocommerce_email_before_order_table', 'add_content', 20 );  function add_content() { echo '<h2 id="h2thanks">Get 20% off</h2><p id="pthanks">Thank you for making this purchase! Come back and use the code "<strong>Back4More</strong>" to receive a 20% discount on your next purchase! Click here to continue shopping.</p>'; }
  Thanks.
          @update 2:  New orders are most of the time in 'on-hold' status, but not in 'Processing'.
   In this case, use this instead:
  add_action( 'woocommerce_email_before_order_table', 'processing_order_mail_message', 20 ); function processing_order_mail_message( $order ) {     if ( empty( $order->get_used_coupons() ) && $order->post_status == 'wc-on-hold' )         echo '<h2 id="h2thanks">Get 20% off</h2><p id="pthanks">Thank you for making this purchase! Come back and use the code "<strong>Back4More</strong>" to receive a 20% discount on your next purchase! Click here to continue shopping.</p>'; }
      Or to handle both 'on-hold' AND 'processing' statuses use this:
  add_action( 'woocommerce_email_before_order_table', 'processing_order_mail_message', 20 ); function processing_order_mail_message( $order ) {     if ( empty( $order->get_used_coupons() ) && ( $order->post_status == 'wc-on-hold' || $order->post_status == 'wc-processing' ) )         echo '<h2 id="h2thanks">Get 20% off</h2><p id="pthanks">Thank you for making this purchase! Come back and use the code "<strong>Back4More</strong>" to receive a 20% discount on your next purchase! Click here to continue shopping.</p>'; }
      This code goes on function.php file of your active child theme or theme
 
  This code is tested and fully functional
  
   TESTING:
   To display the status of the emailed order you can add in the function this line:
  echo '<p>The status of this order is: ' . $order->post_status . '</p>';
      To display the coupons used (if they are some) add this:
  echo '<p>Coupons used in this order are: '; print_r( $order->get_used_coupons() ); echo '</p>'
      (this is just for testing purpose).
 
  
   Original answer:
 
  Yes it is possible easily adding an if statement with 2 conditions. 
  The first one detect if a coupon has not been used in the order used in the order:
  empty( $order->get_used_coupons() )
  And the second one will detect if the order is in "processing" status:
  $order->post_status == 'wc-processing'
  If that conditions are matched, your message is displayed using**'woocommerce_email_before_order_table'** hook:
  Here is your customized code snippet:
  add_action( 'woocommerce_email_before_order_table', 'processing_order_mail_message', 20 ); function processing_order_mail_message( $order ) {     if ( empty( $order->get_used_coupons() ) && $order->post_status == 'wc-processing' )         echo '<h2 id="h2thanks">Get 20% off</h2><p id="pthanks">Thank you for making this purchase! Come back and use the code "<strong>Back4More</strong>" to receive a 20% discount on your next purchase! Click here to continue shopping.</p>'; }
  This code goes on function.php file of your active child theme or theme
  This code is tested and fully functional