Yes it's possible overriding WooCommerce templates (copying the WooCommerce plugin templates folder to your active child theme or theme, renaming it woocommerce).
You can use the same code as the answer of your previous question, but in an other template:
order/order-details-customer.php
that is loaded on Thankyou WooCommerce page ("Order receive" page).
Replace in the portion of code from line 64 to the end on order/order-details-customer.php
template with this code:
<?php
// BEGIN HERE
$shipping_local_pickup = false;
if ( $items_totals = $order->get_order_item_totals() ) {
foreach ( $items_totals as $items_total ) {
if ( $items_total['value'] == 'Local Pickup' && !$shipping_local_pickup ) $shipping_local_pickup = true;
}
}
// END
if ( ! wc_ship_to_billing_address_only() && $order->needs_shipping_address() && !$shipping_local_pickup ) : // HERE TOO ?>
</div><!-- /.col-1 -->
<div class="col-2">
<header class="title">
<h3><?php _e( 'Shipping Address', 'woocommerce' ); ?></h3>
</header>
<address>
<?php echo ( $address = $order->get_formatted_shipping_address() ) ? $address : __( 'N/A', 'woocommerce' ); ?>
</address>
</div><!-- /.col-2 -->
</div><!-- /.col2-set -->
<?php endif; ?>
This is tested and fully functional code
References: