I want to achieve a similar thing to that. For me it's not only posts/categories but also custom posts/categories and events manager events/event categories. And more specifically, I want to be able to see the posts/custom posts/events regardless of the language chosen. In my case, pressing on one category redirects me to the default language.
So I thought, and even opened a topic, what if Polylang let us assign posts to its default category + its counter-language category (that is now hidden).
What do you think?