I don't know for sure, but I think that we can safely assume that there are three-letter acronyms that aren't used. Let's check the amount of possible three-letter acronyms. Since the alphabet has 26 letters, the number of combinations is 26 to the 3rd power, or 17576. That's quite a lot. I'm sure that even without empirical research, we can assume that there are quite a few combinations without any "acronymic" meaning.
Nevertheless, I did some (very) minor-scale "empirical research": In order to find examples of unused acronyms, you shouldn't check combinations with very common letters, but go to the more rare ones. For instance, The following combinations weren't recognised by the web-site you referred to in your question: qqq, xzw, xey, uze & bjf. Those are mere examples. I'm sure that you can find many more.