Yes, if you change the Ship To address for an order in Shopify, that change will update in ShippingEasy during each automatic sync once per hour, or via a manual sync, using the Sync button in the Orders page. Learn more about manually syncing here.
NOTE: orders must remain on the ORDERS page for this automatic update to occur. If the order is moved from the ORDERS page and later returned, it will not receive store updates via the API during an automatic or manual sync.
Can I edit an order in my store after it has synced and have the changes update in ShippingEasy?
How to use ShippingEasy with Shopify
Why are my Shopify orders not syncing?
How are order statuses mapped from Shopify to ShippingEasy?