Sorry, my work computer can not type Chinese.

The answer should be no. Because you take one box from the periodic system to calculate the system potential energy, not the box potential energy. If the equation is as you saying, it double considers the energy contribution between two different boxes. For example, you take box 1 and consider the contribution from box 2, the total potential is U, this U is shared by box 1 and 2, or you will have U on box 1 and U on box 2, the total energy of this two boxes, if you take this two together as one box, the energy is 2U, not U.