ESD strap/mat when working on battery powered devices/PCBs
You have a completely wrong idea about how ESD protection works and why it's set up the way it is.

First of all, "working on device plugged in an outlet" (my god that statement) shall never be done while grounded through ESD protection, it's only done when fully isolated from ground. ESD stands for electrostatic discharge, and refers to stray charge accumulated on (usually) the human body. It can reach up to a few KVe, and it's that spark you sometimes see after walking on a plush carpet and then touching another object - that spark is the charge equalizing between two objects. A lot of electronics is sensitive to this discharge and can be damaged by it. Wrist straps and ESD mats provide a high resistance path to ground to slowly drain this stray charge from your body so that when you reach for that IC chip you don't damage it. 

Battery powered or not, all sensitive electronics handling should happen with ESD controls on place.