If your orthopaedic doctor has recommended non-surgical options, then yes, there is a good chance that you will recover without surgery. Once the elbow has been put back in the position by an orthopaedic doctor, you can keep it in a sling for some weeks.
Physical therapy can help to regain the range of motion and prevent dislocation again. With these measures and the right elbow pain exercises, there is a good chance that you will recover without surgery.