Ordering labs on drug abusers

PalMD poses a really interesting question regarding the medical ethics of running lab tests on a patient to determine if they are drunk:

So here’s a non-life-and-death question: if a patient comes to see you and smells of alcohol, can you add an alcohol level to their blood work without specifically informing them?

As he points out, patients sign a generalized consent for treatment and generally do not expect to micromanage their doctor’s recommendations for tests that need to be run. I would imagine that doctors hardly ever inform their patients, item by item, what will be run on basic blood chemistry and immune panels. I would similarly imagine that should the doctor decide on a followup or two after some initial results s/he might just run them first and tell the patient later if it was a significant health issue.
So why not add a BAL (Blood Alcohol Level; a description of measurements including the familiar blood-alcohol concentration of legal importance) if you suspect a patient has been drinking?