Does the app update Shopify's delivery estimates, the order, or order emails? (Essential Estimated Delivery Date app)

No. Essential Estimated Delivery only shows estimated dates in its own widgets on the product page, cart and checkout.

It does not:

• change the delivery estimates Shopify shows next to shipping methods at checkout
• save the estimated dates to the order (as order notes, attributes or metafields)
• change the Fulfill by date in your Shopify admin
• add the dates to order confirmation emails, invoices or Shopify Flow

To show an estimate at checkout, use the checkout widget (Shopify Plus stores only). This is a Shopify limitation: Shopify only lets apps add blocks to the checkout page on Shopify Plus stores. It is added as a block in the Shopify checkout editor. See How to Set Up checkout placement feature.

If you need the dates on orders or in emails, let us know and we'll add your vote to the feature request.