carbon and ozinizers???

[2 TAZ]

I have an ozininzer which is rarely ever on into the air intake of my protien skimmer. I am running 1/2 cup carbon per 50 gallons. Is it crucially important to have all the water leaving the skimmer pass through the carbon when the ozinizer is on???? I would say about 1/2 or less of the water is now running through it. Any help would be appreciated.