I believe the Seed Box has the same functionality of Looting Bag, Fish Barrel etc.
If the Seed Box is open, any seeds looted will fill into the box first and then the inventory once the seed slots are full in the box.
Apologies for hijacking the comment, just thought it would help enlighten the original comment.
In terms of speed, it's really only expanding the inventory space, so may have an effect on how often the user banks / can take more food for more xp between trips.