There is a growing body of evidence now being accepted in the West that acupuncture may well be an effective treatment for neck pain. Two studies which reviewed all of the trials they could find were cautiously optimistic about the short term benefits of acupuncture treatment and proposed that further long term studies were needed.
That said, you GP is not probably not wrong - by the time that someone is in their 70s or 80s there is often quite a lot of degeneration in the vertebrae in the neck, and if this is causing impingement of some of the nerves emerging at the neck, or tightening of the ligaments and tendons which is itself causing pain, there may be a limit to what acupuncture treatment might be able to achieve. If the restriction of movement is mainly caused by muscles which are guarding to prevent further pain there is a possibility that the treatment may relax them sufficiently to improve the range of movement.
If you do choose to have acupuncture treatment it will be important to establish whether the treatment is providing the same kind of relief for a period but no more on each occasion. Although a practitioner will aim to bring about overall improvement there are times when even a guaranteed period of less pain and easier movement is an acceptable outcome for a patient. This has to be an agreed outcome, though, not simply assumed by either party.