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The plants will be fine. Keep in mind that there are hundreds, if not thousands of strains of algae. The black out does'nt work for every algae. Seeing how the black out method is free, it's always worth a try.
Try and identify what type algae it is. Also, learn basic water chemistry. The best way to ried algae in a tank, is to prevent it in the first place
I've done blackouts twice. Both times for 5 days. No plants died, but some did get rather thin and "streched", like they were "reaching" for the light.