First off, depending on where you live, you might want to check into dispersing fertilizer through your sprinkler system, some cities and townships don't allow it, and some require a special use permit. As for the Chlorine, I would definitely check into weather or not your city or township allows that as well. I wouldn't suggest running any type of chemical through your irrigation system, except those fertilizers which are approved for it. If anything, the chlorine will break down the system components a lot faster than it would help things. There are certain types of fertilizers that can cause problems with your system, such as clogging it, simply stay away from them. Only use fertilizers that are approved and have been tested for use with fertigation. Check out Fertigators products at:
http://www.sprinklerwarehouse.com/SearchResult.aspx?CategoryID=304
I have used these products, both organic and non organic, without any problems.
Tony Posey
Ridge Run Landscapes