I bet that the system will be of little importance, maybe not counting the psychological aspect. The chance that your food will be limited in some way is virtually nil which means that you will most likely still be able to use the long rest every fight. More problematic now, players will feel compelled to search each crate for food. I think in the end, the only thing the system will add is an annoying minigame in management (as if the inventory is not a mess now). There is always a chance that the larian will only place a strictly limited amount of supplies, but this is quite unlikely, especially since then it would make no sense to play characters based on long rest when you have unlimited short rest.
It would be nice if someone tested the system and tried to rest after each fight. Unfortunately, I most likely won't be able to do it myself (lack of time).
