It’s not supposed to, no. Generally when the needles are tapped into the skin you can feel a pinch or a bit of pressure there, rarely pain. However, if a needle brushes past one of your millions of tiny nerve receptors, you are likely to feel that. This is usually instantaneous and when it isn’t, a simply adjustment of the positioning of the needle is usually enough. On the whole, your acupuncture should be not at all invasive.