an impairment of the normal state of the living animal or plant body or one of its parts that interrupts or modifies the performance of the vital functions, is typically manifested by distinguishing signs and symptoms, and is a response to environmental factors (as malnutrition, industrial hazards, or climate), to specific infective agents (as worms, bacteria, or viruses), to inherent defects of the organism (as genetic anomalies), or to combinations of these factors
To me, the description of a disease being that of an "impairment of normal state..." unquestionably describes the addiction model, while the genetic anomaly condition leads to it. So, yes, it fits. I think the problem is that people, in general, like to have their own working definitions of "disease," and that's where things get hairy. And others have doubted a genetic link, but that cannot be soberly espoused these days. Right?