By default, I’d say that would be quite difficult.
However, the Page Header content is just a meta box, so does Polylang give you an option to translate meta boxes into the different languages? If so, you should be able to just translate the Page Header Content itself.
I have the same problem with WPML. There I can translate the custom field field-_meta-generate-page-header-content where GeneratePress stores the content of the page header, but it does not show up. I always get the content in my main language, although the rest of the site is translated.
So is it for sure, that GP’s headers are WPML compatible? So is this an issue for WPML or for you? 🙂