You certainly do not need to completely disassemble the box, although I did the same thing with my first box. I don't think that in necessarily hurts, although folding the diffusion panels nicely can leave noticeable crease-lines in the fabric. I actually think the diffusion looks nicer when crumpled randomly with the rest of the box.
All equipment rental houses and studios fold the boxes with the screens in. Softbox designers are aware of this and design the boxes accordingly. It saves a lot of time with setup and breakdown, especially if you have a lot of boxes.