Compared to the amount of CO2 we add to the atmosphere continuously (still!), I’m quite sure that the CO2 from all the plastic in the ocean is insignificant.
edit: just to make sure that my guess wasn't too far off, I looked up some numbers: we relase about 8 million tons of plastic into the ocean every year. Burning 1 units of plastic produces 3 units of CO2, giving 24 million tons of CO2 if all that plastic were broken down by fungus (or incinerated). We release around 35 billion tons of CO2 every year from burning fossil fuel.
edit: just to make sure that my guess wasn't too far off, I looked up some numbers: we relase about 8 million tons of plastic into the ocean every year. Burning 1 units of plastic produces 3 units of CO2, giving 24 million tons of CO2 if all that plastic were broken down by fungus (or incinerated). We release around 35 billion tons of CO2 every year from burning fossil fuel.