The answer is a resounding yes. When someone is charged with a DUI, they are almost always charged with two separate DUI offenses. The State uses this strategy because it increases their conviction rates; i.e., if they don't get a guilty verdict on one charge, they can still try and get you on the other. In a DUI case where the cops think you are under the influence of alcohol, most of the time a person will be charged with being impaired to operate a motor vehicle at least to the slightest degree, and also with having a Blood Alcohol Concentration (BAC) above a certain amount, either .08, .15, or .20. In a case where it is alleged that a person is impaired by drugs, a similar thing happens. The suspect will be charged with driving while impaired to the slightest degree, as well as driving with the presence of a drug or its metabolite (waste product) in the blood.
But, if you ever find yourself in the situation where you have been charged with a DUI relating to the use of drugs, having a prescription for the drugs may operate as a defense to the DUI drug charge. However, having a prescription for the drugs is not a defense to the impairment charge. The moral of the story is, if you take a medication that could cause side effects that might affect your driving, you must be incredibly cautious while you are operating a vehicle. If you are pulled over, you should protect yourself and immediately call an experienced DUI lawyer who may be able to help show the prosecutor that your conduct was not criminal, and was in fact innocent.