Is it possible to get tennis elbow from being in marching band?

Yes. Tennis elbow is considered a overuse injury. That means that the rate of tissue injury exceeds the body's ability to heal it. The tissue breakdown is cumulative, resulting in chronic pain. Patients typically complain olateral elbow pain, worse with grasping with palm facing down. Depending on what you do in the marching band, you probably could get it from this activity.