I think it would depend on the tank size and how much dilution the chlorine would get. I'm no biology expert though.
When I shock treat our well I turn on a garden hose and let it run for about an hour so that only the chlorine in the house pipes will go to the septic tank. All the chlorine in the well and pressure tank go out the garden hose. I was told that the small amount of chlorine in the house piping will not harm the septic.
That additive works as well as the electronic pest repellants and magnetic water softeners. I pump mine every four years at the least. I have used copper sulfate to kill some vegetation that entered the system, but the rest is a scam.