You have the right idea, but I take issue with the "50% useful" statement. Since the goal of putting a capacitor in an AC circuit is to provide a path for an AC current, it is "useful" 100% of the time, regardless of the instantaneous state of charge at any given instant.
As to leaving a capacitor charged if it is suddenly disconnected from an AC circuit, yes, that can leave the capacitor charged with either polarity. It is common practice to put a high-value resistor across a capacitor in an AC Power circuit to discharge it (bleeder resistor) to minimize shock hazard...