I don't think it will have much impact... once you acknowledge illlegitimate authorities, you're screwed. You have to treat them as parasites for that's what they really are.
For starters, did the Russian people elect Russian authorities? Not. It was just a sector of the Russian people who indirectly elected them and to a great extent because they have no choice and lack enough awareness to organize a popular movemement that would provide them a mechanism to coordinate as a community.
If they had that mechanism, what for would they need "authorities" or companies? They could defacto establish a perfectly workable anarchic system.
As I see it, this movement is nothing but a "lets complain" group or a bunch of "whiners". Once you surrender your capability to decide, to directly participate in making the rules by which the members of your community shall abide and decide to delegate this task to someone else (i.e a state and companies) what do you complain of? What's the point of whining? Shut your trap and obey the masters you have willingly surrendered yourself to. That or fight them.