Am I correct in that if you add more watts, and don't provide sufficient CO2, then algae becomes a problem?

Yes, if you have one element (light, C02, nutrients) out of alignment
or more than the others, the excess can trigger algae blooms.

I'm in the process of setting up a 200G acrylic tank (which has cost me
a fricken fortune so far) and plan to inject CO2. Best of luck with
your tank!

-Kevin