Yes, in most cases. A study of 97 patients with tennis elbow showed that these kinds of treatments often have good results. Patients in this study rested and iced their elbows. They also wore braces and did physical therapy. Some of them took anti-inflammatory drugs. Some also had steroid injections if their pain was severe.
After this treatment, only 25 percent of patients went on to have surgery. What distinguished patients who had surgery from those who did not? Patients who had already tried conservative treatment for sore elbows were twice as likely to have surgery as those who hadn't. Also, patients who still had pain after getting more than one steroid injection were much more likely to have surgery.
Conservative treatment can be helpful, up to a point. If patients don't get some relief early on, they may not be the best candidates for continuing to use this approach.