No, the pH in the reactor should always be 6.2-6.4 and it should be controlled by some type of controller that will read the pH level and turn on the CO2 on a need to basis. Once you have that, then running the effluent should be much easier because the media is constantly melting.
If you don't have a controller and the pH level inside the reactor fluctuates above 6.4, then the media wont melt and you can push as much water as you want through the reactor and you still wont get any increase in Alk or Ca because no media is melting.
Again, the trick is to keep the water inside the reactor chamber at a pH level between 6.2-6.4 and then you can start adjusting your effluent as needed.