No, by default the Customer Accounts Hub app can't see any coupon codes that might be added to an order and instead the re-order button simply checks your inventory for the product and if available, adds it to the cart at the current price of the product.

Any post processing like coupons aren't added as these aren't seen.

Coupon codes can still be added to the order and it is possible to have these added automatically, however the Customer Accounts Hub app isn't part of this process as the re-order button simply adds the product to the cart, if it's available to be added.