Is a sore neck (for an extended period) a symptom of arthritis?

It could be. The neck contains 7 vertabrae and is capable of considerable mobility. Because of this complexity it is a common site for arthritis to develop. However, there are other causes of neck pain including tenonitis, muscle spasm and strain and disc disease. Xrays can tell if significant arthritic changes are pressent. Different tests may be required to determine other causes of pain talk to your doc.
Cause of pain. How did it started, what makes it worse, do you have other pains.