Not penicillin, but yes you can get physically dependent to a drug that doesn't make you "high" and/or without being addicted. And you can get addicted to something that doesn't cause physical dependence (people can get mentally addicted to almost anything, all though of course some things are much more prone to addiction). It's much easier to quit a drug that causes physical dependence than it is to quit an addiction. Even if you are getting withdrawal symptoms if you get no immediate mental benefits from taking the drug and you are not addicted, it is much easier to bear the withdrawal symptoms or control a taper. For example, I quit taking Lamictal and Cymbalta "cold-turkey" and got really bad/weird withdrawal symptoms but I was not compelled to go back to using them.