I am 98.7462 % sure that they do not...in terms of efficacy (and assuming they haven't been exposed to harsh conditions). I have heard that some soaps lose their scnet after a while...but that's just what I've heard.
I lathered up a cake of pashana soap that was at minimum 30 years old. The scent was almost 100% gone, but it lathered up just fine. I ended up grating it and mixing it with 3/1 with a really fragrant bath bar. I still keep it in my rotation. So, to answer the question, 30+ years.