When the camera is on and recording while being attached to an external battery bank, the camera’s battery does not charge. In fact the battery level decreases. It decreases very slowly, but still decreases. The power consumption of the camera is higher then what the external bank can dump into the camera.
The documentation mentions the internal battery life is about 2 hours, and the charging time to full capacity is about 3 hours. So it makes sense that the external charger (even thought it’s a 2.4A charger) can’t deliver enough power to run the camera, let alone run the camera and charge the battery.
This means that the camera can’t be used for an unlimited amount of time, even if plugged into the wall. I don’t know how long the camera can stay on in this mode, but it’s substantially more then just using the onboard battery.
Also, it should be noted that if you want maximum battery life out of the camera, it’s best to plug it in right at the start of the operation of the camera, when the internal battery is fully charged. If you wait until the internal battery is depleted by any amount, an external battery bank or wall plug will be of less use then if the internal battery was full.