Coryza would be considered a growing microorganism, which is why they would typically treat it with an antimicrobial. CS acts more as an antibiotic against bacteria - although some infections can be both.
Like anything natural, I'd say it doesn't hurt to try in most cases. We use something called "super silver" from Amazon.
Some other natural antimicrobials would be cinnamon, pomegranate and spicy peppers. Chickens can't taste "spicy" food, a pepper won't taste "hot" to them. Extracts of these are always good, but doesn't hurt to use a carrier oil, like coconut oil