I came up with many responses to this, but I'll start it with a simple "No, this is not correct."
Before anesthesiology was the pretty, clean science we know today, doctors and surgeons used whatever was popular at the time to numb, disassociate, or render the patient unconscious, using everything from irritant herbs to distract the patient to good ol' brute force trauma. Due to the extreme pain patients experienced, it was not the routine procedure we would imagine today, but a last resort. However, this was due to extreme discomfort to the patient, and the amount of complications that could arise from preforming an operation before our pretty science, which, as you could imagine, was the lack of a sterile environment and insufficient scientific advances to keep the patient alive. It is not plausible that a patient would die of pain, but far more likely from the circumstances causing the pain. More common reactions to extreme pain during surgery would be shock and PTSD, however, the pain did not drive them "completely and utterly insane" as you stated.
Anesthesia awareness is an entirely different bowl of nuts with it's own set of complications, but is not relevant.