Nah, I think they're both going to be like "bow strings". The top cables will remain to hold the posts vertically, in case of shear / horizontal seismic forces. Both will be curved; the bottom cables can't be horizontal -- there would have to be so much tension in them to be horizontal over that span supporting that much weight that I don't think it's physically possible.
There will be trusses spanning between the support point on top of the posts, which in turn will support the ETFE membrane. Anyway, in one of the earlier renderings posted, you can still see the top cables. They're just below the beams that will support the trusses, so they're kind of hard to see.
There's a lot of "tensegrity" voodoo in this structure; some of it doesn't make sense, but if you google that word you'll see some pretty crazy structures / sculptures that don't look physically possible. That said our new building is going to be pretty spectacular, from a design & engineering stand point.