Do I need a 50/60Hz notch filter for battery powered devices?

An ECG circuit picks up 60Hz "common mode" signal from both probes then inverts it and feeds it to the patient's foot to cancel it. The heart does not produce a common mode signal so its output is not affected by the common mode cancellation. Here is the circuit:

_{(Image source: Analog Devices AD620A datasheet (old version))}

Assuming you're talking about the input signal, you may still want the filter because the long leads running to the chest pads (or wherever your detection location is) could pick up a 50/60Hz signal like a transformer's secondary from a nearby loaded mains cable.

If you're only referring to the power supply, you're correct, a battery produces very stable DC voltage, any instantaneous fluctuation in battery voltage would predominantly come from sudden loading/unloading of the battery. Therefore no filter would be needed.