No - the blood cell immune systems are unique to animals, because plants and fungi do not have blood. What they have instead are chemical and physical defenses; plants for example can seal off portions of their vascular tissue (the tissue that conducts water and nutrients through the plant), thus cutting off an infection and stopping it that way. I don't know how fungi do it, but fungi consist of long strings of cells joined to each-other on end in networks, and I'll be their defense system is similar.