http://www.academia.edu/4121636/Stu...n_Health_and_Growth_of_Some_Ornamental_Fishes
If you read the above study, you will conclude that water supplies can have residual contents of up to 2.0 mg/L of chlorine and that concentrations as low as 0.1 mg/L can kill shrimp and other aquatic organisms.
This implies that if one adds just 5% of the tank volume as untreated water, that you can have serious issues.
Of course, this is a generalization of the facts. Some fish species can withstand more chlorine, older fish can withstand more chlorine, some water supplies don't have that high a level of chlorine, some water treatment centers vary the amount of chlorine from day to day or season to season, and some fish, while injured don't actually die within a few days of exposure.
At low levels of chlorine exposure, fish may simply eat less, become more susceptible to other diseases, or pass away earlier than they might have, and in those cases, chronic low level chlorine exposure isn't suspected.
So, one can never be certain from one tank to another, even from one day to another what that maximum % will be.
Given the seriously low cost of treating water for chlorine however, imo, it just seems a better investment to treat all the water.