In the end, though, even Rush calls it an "addiction", which I think we should take to mean that he recognizes that he's taking more than he really needs for some reason other than just pain relief.
YES! If you take any amount long enough you will be addicted. Unless the pain subsides you will need to increase dosage to maintain the same level of pain. Withdrawal from the drug creates a differant kind of pain, that without treatment, nearly as bad, sometimes worse, than the original pain. By medical terms addiction is not the same stigma as it is socially. Many other medications are addictive, doctors often will prescribe addictive medications knowing the patients will become addicted because they consider it the lessor of two evils.