The rate of chemical reactions is based on the instantaneous concentration of the "active" species. It's a probability thing. Imagine lots of "active" molecules bouncing around running into all kinds of organics, bacteria, and algae. When it hits something (in the right way -- with the right orientation and enough energy), it can react with it thereby killing it (if it's a pathogen) or oxidizing it (if it's an organic that doesn't grow) and there are other intermediate reactions, but let's keep this simple. The chlorine that is attached to CYA (as unique compounds) also bumps into these substances, but doesn't react (for a variety of reasons I won't get into here).
In addition to the above, there is an equilibrium between the chlorine attached to CYA and the chlorine that is active and unattached to CYA -- they are going back and forth as well. So if some of the active unattached chlorine gets used up, then there is less of it to get attached to CYA and there is more of it already attached so the net result is that the amount of chlorine attached to CYA will drop somewhat and the amount of chlorine that is active and unattached will increase somewhat to roughly stay in the same proportionate balance. Unless there is a big change, roughly speaking the active amount stays at a constant small proportion of the total amount (the amount measured as Free Chlorine).
So while the chlorine attached to the CYA is clearly available as a "reserve", it is not "active".
You can think of an analogy of people fighting a war where you have a group of "active" soldiers on the front lines fighting hand-to-hand combat with an enemy. You have many more soldiers in the rear that are not directly fighting and are in "reserve". When some soldiers in the front lines get killed or injured, you can replace them with some from the reserve, but the rate at which you will be able to wound or kill the enemy is only dependent on the number of soldiers you have on the front lines doing the hand-to-hand combat. It doesn't matter how many you have in reserve. The amount in reserve only tells you how long you can continue to fight -- not the RATE at which you can fight effectively.
So the key is to have enough soldiers on the front line to kill the enemy faster than the enemy is able to reproduce (double in size) which is what bacteria and algae do. So only the "active" front-line fighters determine whether you can prevent bacteria and algae from growing. The "reserve" is just there so you don't run out until the next time you add more chlorine to beef up both the reserve and the front lines.
Technically speaking, if you could ensure that there was 0.1 ppm Free Chlorine (FC) everywhere in the pool at all times, then that's all you would need to kill bacteria and algae faster than they can reproduce. You wouldn't use any CYA in that case. The fact is that you simply can't maintain such a low chlorine amount as it gets used up locally and circulation isn't good enough to "get replacements" and the chlorine spends a lot of time getting used up combining with organics that are not pathogens (from sweat, leaves, etc.). So to ensure that the chlorine doesn't run out, we use CYA, not only to protect the chlorine from sunlight, but to keep the actual chlorine level low and hold most of it in reserve.
This is the main reason why I believe outdoor pools do not have the problems of indoor pools with regard to disinfection by-products that cause asthma and respiratory illnesses. Indoor pools do not have CYA, yet have chlorine levels of 2 ppm FC or so and therefore have 10-20 times the amount of "active" disinfecting chlorine and therefore degrade swimsuits, skin and hair 10-20 times faster and produce disinfection by-products including trihalomethanes (including chloroform) and chloramines (including nitrogen trichloride) 10-20 times faster. It's true that a lack of good air circulation and a lack of sunlight are other factors, but I believe the 10-20 times faster reaction rates and presumed 10-20 times higher airborne concentrations are more important. I am currently working with the CDC and the top expert on the chlorine/asthma indoor pool issue in England so hopefully we'll be able to see if using some CYA in indoor pools will solve this problem. The CDC is concerned about lowering disinfection levels, but I pointed out it's no worse than what is already done in outdoor pools and I've suggested alternatives to handling the protozoan cysts/oocysts (Giardia, Cryptosporidium) that are hard to kill with chlorine (I'm suggesting using chlorine dioxide which can be produced in a CYA pool easily using sodium chlorite, but the dosages must be pretty precise).
Richard