Does Hyvä Checkout Require The Hyvä Theme?

In short, yes - you will need a Hyvä Theme license in order to use the Hyvä Checkout. This is due to the fact that the theme is a dependency of the checkout as the latter makes use of the features and functionality provided by the former. That being said, the rest of your store pages DO NOT have to implement the theme in order for you to use the checkout, you can use the theme fallback mechanism to configure the checkout to use the Hyvä Default theme.