Will using Thru-The-Body stringing improve tension on the low B? Will making the string path longer between the nut and the tuner improve string tension?
No, and No. These are what I like to call “Bass Urban Legends” They have no basis in reality. The string tension is determined by the pitch, the string physical parameters (mass, thickness, etc), and the scale length (nut to bridge saddle distance). That’s all!! Thru-the-Body stringing can aid sound transfer into the body woods, thus increasing resonance. But it does not increase tension or make for a tighter low B string. And staggering the B tuner further away from the nut on the headstock does nothing for the sound, IMO it’s just a design gimmick.