Hello,
Well, performing both actions, addressing nutrition as well as a blackout, will improve the overall chances of recovery. Improving CO2 and nutrition will fix the root cause of the OP's troubles, however, algae like CO2 and nutrition as well. Nutrition and CO2 are required of all plants, but algae can thrive with very low levels of CO2/Nutrients. They can thrive at low levels.... levels which obliterate plants. So the improvement of nutrition helps the plants to recover from starvation, however plants recovering from starvation does not, in-and-of-itself eliminate the algae that is present. So the blackout functions to remove the light which algae need to produce their food.
So when there is overzealous lighting algae can produce their food. They are very small and need only very small levels of nutrient/CO2. Plants, being much more massive require hundreds or even thousands of times greater mass of nutrient/CO2 in order to produce food for that mass.
Therefore, nutrient/CO2 delivery improvement using injection, dosing, flow/distribution optimization etc., will address the long term health issues of plants and the blackout will help to eliminate the algae that is there. If you do not improve the nutrient/CO2 delivery sufficiently, and have not achieved the long term fix, then the algae will return because their spores are always present in the tank. As soon as the health of the plants deteriorates the spores will be triggered into growth at the drop of a hat. So keeping an algae free tank is all about maximizing the health of the plant. That objective is NEVER achieved by maximizing the light, only ever by maximizing nutrition.
If you have a similar setup in the making, then I highly recommend that you wait until you have the CO2 and fertilizers before flooding the tank. In fact, if you have never run a CO2 tank before I suggest that you flood the tank before you buy plants and just play with the injection technique, dropchecker, diffuser placement and filter outlet positioning. After the few days or a week or so that it takes to figure things out, then drain the tank and plant. This way it allows you to discover the silly mistakes we all make, such as leaks or pinched hoses or gear not responding as we think it should. When you do finally add plants you will have the kinks straightened out and will make fewer mistakes. This will give you plants a better head start.
Cheers,