Adding a memory card to the player is exactly the same as adding a memory card to a computer. You are adding extra electronics that require additional power to operate (whether or not you access access or use it). Memory chips are not designed in a way that allows their data and address lines to remain connected to hot circuitry with their power lines not connected (or turned off). Doing so could damage both sides of the electronics.
As such, anytime you put a memory card into the player it will always drain more power from the battery than without the card.
Beyond that, the amount of power needed to actually access the memory (to play music from it) is very, very little. It’s unlikely that you’d even be able to notice a difference in run time just based on playing all from the internal or all from the external card memory.
It’s really only the fact that the card requires power all the time (regardless if you access it or not) that drains the battery more.
