Will the box float?

It won't float if you place them on top of one another perfectly, which may seem counterintuitive. Normally, you would have a situation where you would have a slight gap between the 2 boxes due to either different materials used or simply because of the formation of oxide on the surface of one material. Then, the water molecules can do their job. However, if you manage to remove all the impurities on the surface, the box will in fact stick. In essence, you can't distinguish that the two boxes are separate and they will appear as 1 box. The same thing happens in case of friction when you try to smoothen a material to reduce friction. After enough smoothening, the 2 materials just get joined together because the molecules can't differentiate that the 2 surfaces are separate. Also, in your example, the slight gap I mentioned previously would also be between the ocean floor and the box. So, even your original box will start to float.