The toadstool leather can easily go a day or two without lighting (even more days). Depending on what type it is, so can the algae.
Green film algae on the glass and cyanobacteria on rocks and sand will somewhat discorporate after 3-4 days of lighting (but are bound to regenerate if the conditions which promote their growth remain in place), but green hair algae can survive a black out of that length.
Nutrient-control is probably the best bet in curbing nuisance algae growth. Algae-eating CUC or fish may work to a degree but they don't address the cause of algae growth.
Rift Lake and Reef tanks.