nope, you have lots of them.not all of them are associated with a hair bearing follicle, but every hair forms initially in a sebacious gland then as it becomes a growth phase hair grows deeper. most vellus hair, ( peach fuzz) grows very close still to the sebacious gland, and if you treat that hair, the gland will surely be damaged, bt your skin isnt going to run out of oil just because we kill some hair.