I once considered keeping some shrimp in an unfiltered tank on a windowsill. I ended up not doing it in the end - I couldn't be bothered going down the whole Walstad route and I didn't want the extra electricity output, but I'm interested in the answer to your question.
I suspect though, the answer is a Walstad kind of thing. Depending on whether you had plants in there, whether those plants got enough lighting, maybe even temperature, pH etc, it's possible that one shrimp on it's own could never produce enough ammonia to poison itself.