The fact that you can mash A and occasionally press B to do most of anything in Pokemon games is part of what makes it so wonderfully multitask-able. I can make dinner, do art, watch a movie, read an article, or even do homework at the same time as playing it, and I'm generally terrible at multitasking.
As far as the story-related bits of an initial play-through, I do definitely keep focused on it and take the time to read, as with important plot-point battles, especially when it's one I've anticipated and I get all into it X3