No. GRAYL's purifier media is not recommended for use with cyanotoxin poisoned drinking water. Cyanotoxins are created when cyanobacteria (or 'blue algae') proliferate in freshwater lakes, under certain conditions, likely exacerbated by global warming. Water containing cyanotoxins is very no bueno for human health.
Activated carbon, one technology in GRAYL's purifier media, can reduce cyanotoxins but not to a level that is sufficient to make the water safe. Reverse osmosis is the only filtration method effective against cyanotoxins.