Dave (a.k.a. Meindzai) directed me to this terrific NPR article, and asked me if I had any experience with the idea of grammatical gender interacting with real gender.
Oh, yes, indeed.
In case you haven't gone over to the article, I'll give you an idea of what it says: people who have grammatical gender in their languages will tend to describe nouns in ways that give them characteristics associated with actual physical genders.
I once read a study (and I wish I could now remember which one) that said that young children who spoke languages with grammatical gender were able to identify their own gender earlier than those who didn't. And, no surprise, children who were asked to assign voices to cartoon characters of objects would give male voices to the grammatically male objects, and female voices to the grammatically female objects. This was not the case with English-speaking kids who haven't had to develop such awareness.
Your native language fundamentally influences how you characterize objects and their relations to one another. For example, a picture is "on" the wall in English, but "up (op)" the wall in Dutch. If you ask friends who speak other languages, you'll be surprised how many tiny subtle differences you'll find.
It might be fascinating to consider putting this distinction, or some other seemingly arbitrary grammatical distinction, into a story. I'm guessing you could get cool misunderstandings, or even disasters similar to that resulting from English vs. metric measurement. I remember hearing that a famous linguist got his inspiration from the idea that words had power over thought, such as when people labeled gasoline cans as "empty" and people were negligent around them, believing they were safe when in fact the gasoline vapor made them far more dangerous around sparks than when they were full.
Feel free to comment, Dave (or anyone else!), if you'd like to further the discussion.