Would an overactive pancreas eventually cause diabetes?

Possibly: I'm not quite sure what you mean when you refer to an 'overactive pancreas' but one of the theories for why diabetes occurs is when the pancreas has to work too hard producing insulin in people who are overweight. Eventually it wears itself out and there is insufficient insulin for the body's requirement which results in diabetes. Perhaps this is what you mean?

Diabetes: Pancreas is a gland that produces enzymes important for digestion and also the insulin, hormone, that utilises sugar Diabetes results usually from either destruction of the cells within the pancreas that produce insulin, in case of Type 1, or when the insulin receptors inside target cells do not respond to the insulin, or Type 2