Adversarial machine learning, focused on studying various attacks and defenses on machine learning (ML) models, is rapidly gaining importance as ML is increasingly being adopted for optimizing wireless systems such as Open Radio Access Networks (O-RAN). A comprehensive modeling of the security threats and the demonstration of adversarial attacks and defenses on practical AI based O-RAN systems is still in its nascent stages. We begin by conducting threat modeling to pinpoint attack surfaces in O-RAN using an ML-based Connection management application (xApp) as an example. The xApp uses a Graph Neural Network trained using Deep Reinforcement Learning and achieves on average 54% improvement in the coverage rate measured as the 5th percentile user data rates. We then formulate and demonstrate evasion attacks that degrade the coverage rates by as much as 50% through injecting bounded noise at different threat surfaces including the open wireless medium itself. Crucially, we also compare and contrast the effectiveness of such attacks on the ML-based xApp and a non-ML based heuristic. We finally develop and demonstrate robust training-based defenses against the challenging physical/jamming-based attacks and show a 15% improvement in the coverage rates when compared to employing no defense over a range of noise budgets