import bpy

MATERIAL_NAME = "Material"

mat = bpy.data.materials.get(MATERIAL_NAME)

bpy.ops.object.select_linked(type='MATERIAL')

sel = bpy.context.selected_objects

for ob in sel:
    if ob.data.materials:
        # assign to 1st material slot
        ob.data.materials[0] = mat
    else:
        # no slots
        ob.data.materials.append(mat)