Is it possible to get nerve damage from acupuncture?

Yes: If the acupuncture needle sticks a nerve and is moved around. The needles should not be placed near a nerve.

Possible effect: Yes, if a needle was placed directly in a nerve it could cause damage. Luckily that is uncommon. The needle tip is placed close to the nerve to "grab chi" or contact it's electric field. A patient would feel pain if the needle were approaching the nerve too closely. A gentle needler would stop progressing the needle at that point & avert nerve damage.