Not necessarily. It may even increase, since the strings then become an ungrounded antenna. Typically, with conventional strings and a passive bass, the player's hands and body become the final ground to eliminate the noise. The nylon tape is an insulator that eliminates the direct metal-to-body contact, and hence the grounding.
I would keep it strung body-through and shield the passive bass control cavity.
Another option that I have on my mid pickup on my passive bass with nylon tapewounds is to install a grounded chrome pickup cover , so my thumb anchor also functions as the string ground like a bridge ground conventionally does.
Or the final solution, which I use on my gigging party band bass, is to go EMG actives, which are internally grounded, don't use a bridge ground, and have a greater than -100dB noise floor. The string configuration is then a moot point.