I haven't seen shielding coils on my 59 / Custom or other Trembuckers.
Are you talking about the shielding around the wires inside the plastic sheath or the fifth, bare, wire inside the sheath?
The screening inside the sheath is there to (1) stop the individual wires picking up hum between the pickup and the ends, and (2) because, I suspect, the cables they buy come like that anyway. It holds the individual wires together before the outer sheath is extruded on, and stops the individual wires' insulation from sticking to the sheath.
The bare wire / baseplate ground stops the baseplate from transferring hum or eddy currents. It makes contact with the screening foil inside the cable all along their lengths. Note, however, the bare wire should always go directly to ground on the back of a pot casing, never to a switch or pot terminal.