I have a full body, bodyweight workout could doing this three times a week lead to overtraining because training all muscles three times in a week?

Listen to your body: The quick answer is no with the following caveats. Adequate rest between workouts along with a balanced and healthy diet is essential to limit the probability and ill effects of over training. A strong core (abdominal muscles) is essential and can be part of a daily exercise regimen. Listening to your body and taking a holistic approach is key.