Display a text message if the shortcode is found?

Try this:

<article>

                <div class="entry-content">
                <?php
                $current_user = wp_get_current_user();

                if ( isset( $current_user->user_email ) ) {
                    echo '<p>' . sprintf( __( '%s, here is your client area', 'my-theme' ), $current_user->display_name ) . ':</p>';


                    $output = do_shortcode( '[picu_list_collections email="' . $current_user->user_email . '"]' );

                    // the shortcode returns an empty <ul> tag, if there is no gallery 
                   // https://plugins.trac.wordpress.org/browser/picu/trunk/frontend/includes/picu-template-functions.php#L464

                   if($output == '<ul class="picu-collection-list"></ul>') {
                        echo '<div class="woocommerce-MyAccount-content">
                                 <div class="woocommerce-notices-wrapper"></div>
                                 <div class="woocommerce-Message woocommerce-Message--info woocommerce-info">
                                   There is no gallery.
                                </div>
                             </div>';
                   }
                   else {
                       echo '<div class="woocommerce-MyAccount-content">
                                <div class="woocommerce-notices-wrapper"></div>
                                <div class="woocommerce-Message woocommerce-Message--info woocommerce-info">
                                    Your gallery.
                                </div>
                         </div>';
                       echo $output;
                  }
  }

                ?>
                </div>
            </article>