I can’t speak for this device in particular, but often the battery terminals pass through a boost circuit (DC to DC voltage conversion). This then passes to the same circuit as the DC input is routed (power filtering and voltage regulation). This is because batteries tend to run at lower voltage than the DC. Voltage regulators typically need some voltage headroom above their output on the input, so if you don’t boost the voltage of the batteries they will cut out while still providing more power than is required to run the device.
As an example, a working NiMH battery might output 1.2V: 6 batteries give 6x1.2 =7.2V; a set of fresh alkaline cells might provide 9V; the voltage at which either cell is “dead” is about 1V, which puts the output at around 6V (which is the lower voltage bound for most 5V regulators).
That all being said, the battery terminals probably never see 9V. The boost circuit is probably okay with this, but I’d recommend checking it out to confirm. Someone may already know this, but identifying the boost circuit and checking the data sheet would be possible. If you are unsure, another option is to send power to the DC points where the jack connects to the PCB (no need for the jack).