I think the missing key to this question is identifying what discrete aspect-of-tendency is actually behind that anti-voting position. Because it's not just anarchists, and we all know these categorizations have ill-defined boundaries. Yes, it's clearly a question of authority and critique of representation (as opposed to delegation, etc.); these are very much in the domain of anarchist concern, and it does seem to be mostly anarchists voicing that position, but I have to wonder how much of the perception that it's an anarchist thing is just a bias toward fitting the subject to the stereotype. I have known / heard from a ton of people who describe themselves actually in opposition to anarchy having basically the exact same position (against participation in US elections), for the same reasons—framed as a rejection of tacitly supporting neocolonial empire, of distracting people from what could otherwise be an impetus to organize, and so on. Often these people are like vanguardist online revolutionaries with an urgency to match the direly moral seriousness of voting or not. It's the same vibe whatever you believe. You can probably find conservative constitutionalist weirdos who won't stoop to vote in this sham version of their country. [EDIT: It seems, then, to be more of a question of absolutism, of urgency of moral imperative. Or, you could frame it as a difference between of theory vs. practice in any given individual's choice of lifestyle/focus. And we need both those kinds of people.] To me, this says the that yes/no answer to the question is pretty superficial. But asking the question that you're asking is not, if we can use it to look deeper.
For me personally, I vote or don't vote depending on whether I feel it's practical or necessary, i.e. how useful my participation is, vs. how damaging it feels to the situation or to my sanity to take that compromise, or just based on how mad I am. I simply have a lot of resentment about the idea, from any quarter of the left, and not just in voting, that I am morally obligated to participate in something that I find pretty revolting. But like I'll do it, if it helps to prevent or slow a slide into fascism.