Cut the CO2 during the blackout. Your plants can only utilize it during a bright photoperiod.
Here is my blackout protocol:
1] Immediately before the blackout do a 50% water change
2] Add some airstones or powerheads to the tank if possible, but by all means maintain standard filtration
3] Cover the tank so that no light can enter
4] Turn off your heaters so that mean water temp stays below 77F
5] Do not feed, fertilize, or inject CO2 for the duration of the blackout
6] Don't peek
7] 3-5 days later uncover it and enjoy feeding your starving fish and plants that have no algea
8] As soon as you uncover the tank, do a 50-75% water change to remove the dead algae