Never bother to find out, but I think "in theory", yes. That would also depend on how much cualerpa you have in comparison to the total water volume. If it's only a relatively small patch versus the whole sumpfull of caulerpa, then it shouldn't make that much differences.
Now, I wonder if CO2 retention rate in our tanks depend more on algae consumption, or does it depend more on gas exchanges, meaning gas exchanges provided by surface water movement, protein skimmer, and (in many people's case) 6 foot drop down to the sump?
If the CO2 retention rate depend more on the gas exchanges, then the algae CO2 consumption would be insignificant, and thus means light cycle can be set either way.