Yes — the app does support Shopify Automatic Discounts.
Turn on this feature to apply applicable discounts automatically for customers during checkout.

NOTE: If the new draft order flow is not enabled within the App setting, the Automatic discount only applies on the Product base price. In order to apply discount on total amount of order that inlcludes add on charges, please enable below from Settings>>General Settings>>Use new draft order flow
Outcome: 
There are a few limitations when using Shopify Automatic Discount codes with the Hulk Product Options app, primarily due to how option charges and existing variant charge types are handled between the cart page and checkout.
Minimum Purchase Amount Discounts
For automatic discounts with a minimum purchase amount, option charges are not considered on the cart page, but they are correctly applied at checkout.
If the main product price (or the updated total after quantity changes) alone meets the minimum purchase amount, the discount will appear on the cart page and match the checkout total.
Discounts on Products Using Existing Variant Charge Type
When an automatic discount applies to products added using an existing variant charge type, the discount may not display on the cart page, but it will work at checkout.
Fixed amount off: The discount applies to the main product on the cart page, while the discount for the variant-based option appears only at checkout.
Percentage off: The discount applies to both the main product and the variant-based option on both the cart page and checkout (if included in the discount).
Buy X Get Y Discounts
Automatic Buy X Get Y discounts with a minimum purchase amount are applied only at checkout.
Buy X Get Y discounts with a minimum quantity requirement or “at a discounted value” settings are also applied only at checkout.
Discount Eligibility for Variant-Based Options
Products added using an existing variant charge type that are not included in an automatic discount will not be counted toward the discount.
For Buy X Get Y discounts, if product Y includes an existing variant charge type option, it will not be discounted unless:
It is explicitly included in the Y products list, and
The correct quantity of Y products is configured.