It certainly sounds possible..and as Sj mentioned you can be negative forever since that has been the case with me. I have been seeing my rheumy well past three years now, and have never had a postive test for anything. I came down with a virus and a few weeks later the joint pain started and that was it for me, here I am. My rheumy now says the word.."rheumatoid" and I also had the swollen joints before I started taking the stronger medications. I think another poster mentioned the Plaquenil and that is a fabulous one when you are first starting out, it does wonders for the fatigue. However, if you do take it, make sure you make an appointment for an eye exam before you begin taking it, since it can cause damage to your eyes (this is extremely rare) but I was one of those rare cases.
Please keep in mind that a good doctor will treat your symptoms and not just your test results.