Question is in the title, I am interested in your thoughts...
I believe Come-from-Beyond who is one of the lead NXT devs (not to be confused with Come-from-Above) is (was?) working on a design for a distributed ternary logic processor called Jinn. If you're interested in the subject then that might be worth looking into.
As for my opinion, I'm not sure if there is any significant benefit although I'm not a specialist in the field so my opinion probably doesn't mean much. Having an additional state probably complicates things on a hardware level and anything that specifically calls for a ternary design could probably be implemented using binary logic anyway.