Coryza is not transmitted through eggs. Survivors are carriers of the disease and will spread it when stressed. There isnt any immunity to the disease. Coryza is easily spread via feeders, waterers, clothing, sneezing birds etc...
If you decide not to cull sick birds, there will come a time that sulmet and antibiotics wont work due to resistance by the disease itself. Then you'll have to purchase other types of antibiotics, most likely more expensive and more powerful, to treat (but not cure) your birds. It's also possible that mycoplasma gallisepticum could be involved in conjunction with coryza. Consider having your sickest bird sent off for necropsy to find out exactly what you're dealing with. You can contact your local extension office or state agriculture department to find out how to go about doing that. Good luck.