Yes, the app works with both types of themes.
Both theme types support the App Embed Block. Once you turn it on in the theme editor, the app is active on your store.
There are two App Blocks available:
Associated Fees shows the fees that apply to a product on the product page.
Fees Total shows a message on the cart page if fees apply.
If you’re using an Online Store 2.0 theme, you can add these blocks using the theme editor.
If you’re using a legacy theme, you can add them by pasting <fees-total></fees-total> or <associated-fees></associated-fees> into your theme files.