I also have a planted tank.. i've not bothered to injected it with CO2 for well over 2 years... and the plants still grow like crazy...
Aquatic plants (freshwater) can draw on other forms of carbon, namely dissolved organic carbons as compared to only dissolved CO2 gas... I believe macroalgae will be able to do the same as well... i do not believe that the ocean contains a lot of dissolved CO2 gas anyways...
Well if you don't believe us why don't you try to inject the CO2 into your refugium and see for yourself...
I too tried several types of macroalgae before, sea lettuce, calpura etc... but they never seemed to survived for long, after several tries only an unidentifiable macroalgae survived and thrived in my refugium...