Not really. Older cards drew more current than new ones (and had less storage). The card is accessed one block at a time, so whether there are a few of them or a lot of them really doesn't change the amount of current used when accessing a block of the card. Of course, if you have a 256GB card full of movies, it's going to eat a lot of batteries watching all of them, but that's not due to the size of the card, it's due to the fact that you can be using it more.