If the horse is alert and holding his head up looking out of the halter, he may present a more desirable picture to the judge for evaluation. Even though the horse may not be disqualified, he may not place as high as he could have just because he does not present himself well.
It may be difficult to train your horse to be alert, but you can work with him to hold his head and neck at the most desirable location to enhance his conformation. Practicing and spending hours getting your horse used to standing in the square position may increase your horse's endurance to remain alert for longer periods of time.