One of the most bizarre things I ever experienced was an active guitar I built that, at one point, had radio frequency interference issues. I lived rather close to a huge AM radio antenna farm, and one day, I had AM radio coming out of my (previously silent) guitar. Oddly, it was far better sounding than most AM radios - very good fidelity of the unwanted signal. The thing didn't have too many components, but at one point I had changed them all, and the AM radio persisted in coming through.
So I tried (in desperation) a different battery. Silence. Swapped the battery back and forth a couple times so be certain, but yes, somewhere in that battery was a poor contact acting as an RF detector. If you're trying to shield against interference (electrostatic and.or RF), yes, even the battery should be shielded. Another takeaway is that and active bass has to be done right, or someday you may have RF issues - active electronics (and batteries) can be RF detectors, passive circuits don't do that.