Not necessarily. A recent study examined the elbow joints of 136 male college athletes. Over one-third played sports that required overhand actions, such as baseball and tennis.
Participants had both elbows tested in a device that pushed against the forearm, angling the elbow outward. An X-ray showed how far the joint separated, suggesting how well the ulnar collateral ligament on the inside edge of the elbow held under pressure. This is the ligament mainly responsible for securing the elbow so it isn't easily strained into this outward position.
To visualize this angle, straighten your arm with your palm up. Now try to make your forearm angle out to the side where it meets the elbow joint. In a healthy elbow, the ulnar collateral ligament makes this action nearly impossible.
There were no major differences between players, even the ones doing overhand sports and those who had been playing for many years. These findings led the authors of the study to conclude that extra laxity of the elbow doesn't occur in athletes who participate in such sports but are free of elbow pain.