Do your best to clean it out. Sometimes I get lazy and put it off for a few days after a cook, but its my understanding that ash + moisture can lead to the ceramic lining eating away.
If you let it get too full, it affects the air flow around the coals on the grate. You could probably get by with not emptying the ash after one cook, but I would not go beyond that.
I always try to clean my WSMs the next day after a cook.
I save all the charcoal peices that don't fall through the grate for the next cook. I then dump the ashes and brush the bottom out.