Since you have such an infestation and cyano is a bacteria which contains some of the characteristics of plants....the bottom line for treatment is it is not a plant or an algae. And bacteria's....even blue-green cyano....need to be treated for complete eradication for your safety as well as the fishes. They are predominantly light-dependent organisms, but they are also capable of a using organic compounds as a source of energy. I think it will come back.
Found this from the WA state dept. of health:
What causes a bloom?
Factors needed for bloom formation - whether toxic or not - are complex. No individual environmental cause or particular set of conditions clearly controls cyanobacterial bloom formation. Researchers have investigated factors such as light, temperature, percent oxygen saturation, nutrient availability and depletion, wind patterns, internal lake mixing, growth stage and zooplankton predation.
Three genera of cyanobacteria account for the vast majority of blooms: Microcystis, Anabaena, and Aphanizomenon. A bloom can consist of one or a mixture of two or more genera of cyanobacteria.
Cyanobacteria cannot maintain an abnormally high population for long and will rapidly die and disappear after 1-2 weeks. If conditions remain favorable, another bloom can replace the previous one in such a way that it may appear as if one continuous bloom occurs for up to several months.
What kind of water treatment removes cyanobacterial toxins ?
According to EPA, water treatment techniques such as coagulation, sedimentation, filtration, disinfection, granular activated carbon, powdered activated carbon, ozonation, and ultraviolet radiation are effective to varying degrees at removing most common cyanobacteria and their toxins in drinking water. Close to 100 percent of particular toxins can be eliminated in finished water when the appropriate combination of techniques is used.
And you may my prolongingly exposing your fish to it which may result in internal organ damage for them. If it accumulates in the organs of fish from lakes, ponds and rivers....it will accumulate in the organs of your aquarium fish don't you think?.....
Can I eat fish from contaminated water?
Microcystins can accumulate in fish tissues, especially in the viscera (liver, kidneys, etc.). Concentrations in the tissues would depend on the bloom severity where the fish was caught. Take caution when considering consumption of fish caught in a water body where major cyanobacterial blooms occur. Before eating, remove the internal organs, which may contain more of the algae/toxin.