You dont have to remove the carbon when adding co2 per se, however if you are adding co2 to benefit the plants adding carbon will remove lots of the nutrient the plants need to grow. So in effect you adding one nutrient whilst removing others, might as well given them all of them!
i use a solenoid on the same timer as my lights. With the CO2 off at night my pH rises by .4 with no effect on the tank occupants. The solenoid makes the set up more expensive, but with a 10 hour photoperiod I use less than half the CO2 of a 24/7 system.