I would carry it on, uncharged with the charger…and carry the manual with you also if you have one. If you put it in your checked luggage it’ll most likely get inspected by TSA and guaranteed they’ll break it open or keep it…if you carry it on dead you can at least explain to the agent what it is and what you’re using it for….
not sure about a transponder, but when I’ve flown with electronics, they’ve always asked me to turn it on. perhaps to show it’s not a laptop/camcorder shell loaded with explosives
I’d keep a charge on it, at least to show it works. manual, or a website on your phone ready to show them should suffice