You are correct, more or less. However, and I'm know I'm being anal here, what you are describing is a currency unit; not money. And the use of a money arises first in the absence of coercive forces such as a government. A socialist anarchy is impossible, because capitalism is the natural extension of individuals exercising their right to trade the fruits of their own labors. If a socialist society were to form from an otherwise anarchist society, one of two things will happen. Either the best efforts of the majority (seeking the greater good) will be undermined by a minority (seeking only their own best interests), such as was entertainingly described in the movie Star Trek Insurrection, resulting in the rise of a warrior class (and therefore a peasent class) ultimately leading to the formation of a monarchy.(all warrior classes form rank structures, the guy with the highest rank is the monarch by default) Or the first generation of social anarchists will wisely foresee this flaw in their own logic, and found some institution intended to organize the collective forces within society to oppose the rise of gangs or any other warrior class that is not beholden to the socialist collective. In which case, they have just established a government, and are no longer anarchists.
Love it!!
True anarchy as a political structure is unsustainable, and will always lead to something else entirely. Most self-described anarchists are aware of this, and therefore are not really anarchists; but instead are whatever kind of idealist that they expect would come from the anarchy. Anarchy is simply a temporary condition; the time period between the final collapse of the current condition and the initiation of the intended political structure. Karl Marx was, himself, aware of this and regarded a forced state in anarchy as a necessary step towards his communist ideal. Historicly, they are all wrong. Anarchy has always led to the formation of warrior classes taking control of territories, whether you call them gangs, warlords or freedom fighters.
Also true but what I found surprising was that Anarchy existed for hundreds of years in many regions before warrior classes could be established so that they could gain dominance and form monarchies.