To answer your question, I asked Dr. Jim Adaskaveg, an expert in disease control and use of fungicides for produce.  Following is his response.

 "We have found that some fungicides are unaffected by sodium hypochlorite (e.g., fludioxonil, propiconazole, TBZ); whereas others are affected and degraded rapidly (e.g., pyrimethanil, imazalil). I have never tested iprodione but I am guessing that it is probably unstable. If it is degraded, the reaction is fairly quick. We measured residues of fungicide in a aqueous solution with and without 100 ppm sodium hypochlorite after a few hours. If the same amount is present then no degradation occurs. We then did efficacy trials with inoculated fruit using the same treatments to ensure the activity of the fungicide was not lost and that the solutions were not phytotoxic. This is published in Plant Disease 92: 261-269."

Iprodione is the chemical name for Rovral.  It seems Dr. Adaskaveg feels it is not a good idea to mix Rovral with chlorine, however he has never tested it. He suggests that you could try making the mixture and then having the efficacy of the solution tested as compared to fungicide without chlorine.  This will give you the final answer.          

-Beth Mitcham