No, the damage is being done by a yellow-bellied sapsucker (Sphyrapicus varius),  related to the woodpecker. This federally protected bird searches shrubs and trees with thin bark and pecks rows of holes in a distinct pattern. Sapsuckers feed on the sap that flows from the hole. Healthy wax myrtles can sustain a large number of holes without any apparent damage. You can apply an approved bird repellent to the trunks to discourage its activity. Resources:   Woodpeckers

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