Close. You don't have a right to operate, you have permission to operate, subject, as you say, to informed consent. If you had the right to operate, the patient's consent wouldn't be an issue. You have the right to speak freely, without the consent even of those about or to whom you're speaking. Big difference.
And, as a patient, I would deny consent if I thought you were not competent for whatever reason, be it fatigue, intoxication, or just plain being a lousy doctor. Informed consent requires that the patient understand the risks to which he is being subjected. Your fatigue--or drunkenness, or your six trips to the review board--are a relevant risk.