I don’t know colregs better than you all but as a long time sailor I have read them that if your engine is turned over (in neutral) in a situation like this you would be considered a power driven vessel. The reason being is in this case if that vessel “adrift” can see it appears to be under power because of the exhaust and water coming out the transom.
Also, Hogsnort, sorry but I have not recently (within the past 16 years) seen a boat racing with its engine on for the allowable rule that you state (I used to race, but it has been a few years). Also, that may have been true decades ago when batteries didn’t have the bankable capacity they do today (such as AGMs) we also have solar cheaply now (and more energy efficient systems, example, LED interior and running lights). We don’t even have AGMs aboard, just group 27 nothing special, and a small solar panel and never have needed the engine to keeps things up and running, including our large refrigerator that keeps ice cream. Only use the gemny at anchor after a couple of days.