Hi, I've registered just to answer this topic. I know anecdotal evidence isn't worth much, but that seems to be what most people here use anyway, so I guess it fits. Yes, I think acne can be "cured" by fasting. It seems to have fixed mine. Sorry about the wall of text to follow.
I've been fighting acne for ten (!) years and I've tried everything doctors would offer me (I haven't heard of anything I haven't tried, anyway). I also attempted a good deal of homemade remedies and dietary changes, as hard as it was considering that everyone seems to have different beliefs on this or that being *the* culprit (usually with zero evidence for support). I used all sorts of anti-acne cosmetics and then ditched all of them, using only the mildest micellar fluid I could find. The only thing that seemed to improve my acne, but still didn't fix it, was restricting high GI carbs.
Guess what? A while ago I've heard of IF and attempted it, never considering it could influence acne. I did the "lite" version, so called 5+2 (eating <500 kcal two days in the week and not restricting yourself the rest of the week). You can imagine my surprise when after two weeks, I had no new acne changes on my skin. None. Whatsoever. For the first time in ten years. I've been eating fruits the whole time, had some starch from quinoa and oatmeal, even experimented with having some sugar, and I have no new breakouts so far.
My hypotheses as to why it worked for me revolve around mild case of SIBO (I have *no* gastric issues whatsoever, so it's kind of unlikely) or simply fixing my metabolism somehow. I don't know if that's the case, but I'm glad it worked. I'll come back and update this post if there's a remission and it turns out to be ineffective in the long run, of course, but somehow I don't think it's coming.
TL;DR Yes, it seems it can cure acne.