No - Fungus. Should be branched, colorless filaments. Usually attached to some piece of decaying matter - may form a fuzzy coating on or around an object. In water, some bacterial infections of fish and other animals may be mistaken for a fungus. Most likely Protista.
Most green protists are flagellates, that is, they move rapidly with a spiralling motion.
Unless you get them to stop, you can't really see the flagella. Watch out for colonial protists, though, such as Volvox, which forms a spinning ball of green cells. Don't be fooled into thinking it is a plant. Remember, the more you observe the organism, the more sure you can be. Many living things have stages that make them resemble members of another kingdom.