Any conductive part in your circuit will be subject to picking up electromagnetic noise. That includes wiring and other compoents. A humbcuking pickup only protects you from noise picked up by the pickup - if you have unshielded wiring (as in your photo), the wiring itself may still pick up enough noise to make you unhappy. That's where shielding a cavity helps, and it has nothing at all to do with the style of bass or the type of pickup in it.
I haven't seen one of those close up so I can't tell for sure, but I know some instruments are given shielding paint in the cavities prior to their final finish, so the fact that the green extends into the cavity doesn't mean it isn't shielded.
Ultimately, the question "does this need shielding?" is best answered by observation: does the bass make noise in your normal playing conditions?