Well most sleeping things if you hit them will wake up so if it does not react you probably knocked it out.
Also even without perception modifiers the animal comanion should have scent and the ability to notice you within 30 feet and pinpoint you within 5 feet. And you wont be able to sneak attack the barbarian unless he is immobilized, (yes he can comically avoid sneak attack damage while asleep )
EDIT: ^ even a character optimized for spotting has less potential modifiers then a character that is invisable and skilled at hiding.