I just tested my Bridge JBXN, full on volume , Neck pup turned off, and rotated the tone knob full on and rolled off, and there wasn't any hum. Preamp and Power amp wound up too, so i guess you needn't worry.
I dont know much about electronics, so i dont know if the pots have anything to do with helping single coil pups to hum, but I changed the pots in mine to Bourns pots, the Rolls Royce of potentiometers, and i did
that long before i fitted the Entwistle neo pups. So the Bourns pots may ( or may not ) be helping to eliminate hum, but i couldn't say. There's only the regular back shielding paint in the control cavity ( presumbaly done by the builder during construction ) but i havent added any other form of hum cancelling stuff