The words "never" and "anything" are somewhat restrictive (and we know that absolute statements are always wrong). Nowadays, you can't be recognized at all when you're not publishing. Additionally, the term "Genius" is hard to define...
One person came to my mind is Grigori Yakovlevich Perelman. He hardly published anything, did not even defend his dissertation, and was one of the few leading researchers at his institute who only was a "PhD candidate". Of course, strictly speaking, he did publish something, particularly his proof of a generalization of the Poincaré conjecture. But this was not published in some mathematical Journal, but only on arXiv.
I think that someone who casually finds a proof for a generalization of a conjecture that dozens of mathematicians had been working on for 98 years, and doesn't give a ... care about the formal process of scientific publications qualifies as a genius, and is close enough to "never publishing anything" to be mentioned here, at least...