Writing _good_ documentation absolutely can be just as tiring as creating the thing being documented. It's quite common to not particularly value documentation quality and be happy with a mess of words churned out with little thought because at least it exists, but ensuring that it's accurate, covers all of the little details, and is organized well requires some careful thought and editing processes.

With a formal division between "deep thought" work and "easy" work, I'd be inclined to churn out a rough draft of documentation in the second time box but then spend at least as much time as that in the first time box cleaning it up.