It doesn't seem to. I've had several plates of ambrosia in a chest for a bit over a week game time, and it's just as good as it was when it went in. It's like time completely stops for anything put inside it (paintings, photographs and nectar won't increase in value if they're inside a chest). The up-side is that this works well for ambrosia in a dynasty, since sims will not go and interact with a chest unless they're told to, so you don't have to worry about a non-immortal grabbing some when you're not looking.
The down side is that it would not work well as a regular refrigerator, for the exact same reason. Also, you can't cook food at all without a fridge, even if you have all the required ingredients in your inventory.