As stated, produce (both veggies and fish) do not go bad. But here's an interesting thing about those chests:
Anything stored in a chest is effectively frozen in time. You can even store prepared meals in there, and they won't go bad. However, you lose the convenience of sending the sim to the refrigerator to remove a single serving of a group meal. Anything placed in there must be removed manually and placed on a surface so it can be consumed. But this is very handy for storing meals that you don't want your Sims to autonomously snack on (like Ambrosia).
Also, if you would be so kind as to change the title of your thread so that it better reflects what your thread is about, it would be appreciated by the staff. Making the title more descriptive increases the chances that someone will actually look at your thread, since the viewers will have a better idea as to whether or not they have something to add or if the topic is of any interest to them. Had I not been a moderator, I probably wouldn't have even looked at it.