That's a whole lot of assumptions that need to be true for something like this to happen. The biggest assumption is that after the anarchist revolution the overwhelming majority of the populace will become ideologically anarchist and will refuse counter revolutionary propaganda and agitation. This has never happened after any revolution in history, in a lot of cases only a few percent of the populace were committed revolutionaries that actually execute the revolution with only the conditional backing of a huge chunk of the populace.
If anarchism can only work if most of the people are anarchists it's not a viable revolutionary ideology IMO.