Expect it to be crowded. In a mere two months, approximately 300,000 climbers attempt the climb up Fuji annually. So what does crowded mean in the Japanese sense of the term? During the peak of the climbing season, between mid July through to late August, it is common to be lined up shoulder to shoulder on long bunk beds. This is a fact especially on weekends, when climbers will also arrive at all hours of the night.
It is best to view your mountain hut stay as a period of rest, rather then expecting a good solid sleep. It is important and beneficial however to rest your body, even if it means little sleep, before making the final push to the summit rather then attempt the climb all in one push over night.