I don't think this would have been true, at least in that time and place. Warfare in Archaic Greece -- i.e. when Homer was writing -- was dominated by hoplites, expensively equipped heavy infantry drawn from the citizen classes. Later on, peltasts and other light infantry became more common, and were sometimes recruited from unfree classes (especially in Sparta, which fielded large numbers of helot auxiliaries), but also came as mercenaries or from the lower free classes.