It's an interesting thought, but:

When you do two googles, of "eye twitching" along with either "botox" or "acupuncture", you'll find lots of talk in forums about acupuncture and lots of medical / treatment sites describing botox use. I don't know what to make of that, but it's suggestive imo.

If I were seeking treatment, the appeal of injecting botox in an area is that there seems way less precision and skill needed when compared to using an extremely tiny acupuncture needle hoping to coincidentally impact or end up beside a similarly tiny nerve (and nerve placement varies considerably from person to person), out of sight beneath the skin.

So to my way of thinking, there's way less skill needed by the practictioner. If both methods could work as I imagine they do (though I'm puzzled at why the acupuncture needle would be placed in the hand), it just seems more likely to me that results will happen with botox. It sounds like you're fortunate enough to have an extremely skilled acupuncturist in your area.

Don