The first recorded successful appendectomy was done in 1735 by Claudius Amyand. Without operation or antibiotics, most patients with acute appendicitis die. The Merck Manual lists fatality rate as > 50%, but no exact numbers. So, it wasn't an automatic death sentence, but the prognosis was not good.

You said "safely operated", and operations done before widespread use of antiseptics (pioneered by Ignaz Semmelweis, 1847) were far from safe. So, most people who got appendicitis in that period died either from the disease, or from infection after the operation. There is no cutoff date, obviously, patients' chances improved with the advances of modern medicine (antiseptics, general hygiene, anaesthesia, antibiotics, etc.). Although even today, some people die from appendectomy (less than 1%).

If you are interested in medical historical issues, you might like Gerald Imber's biography of William Halsted Genius on the Edge.

He didn't invent antiseptic surgery, but promoted it more so than most in the field. Imber's description of surgery before antisepsis (and before wide-spread use of anesthesia) is pretty chilling.

He also points out that the use of anesthesia became common much more quickly than antisepsis, and theorizes that this was because anesthesia made the doctors life better immediately (less yelling) whereas antisepsis was kind of a pain for them (washing hands with an acid solution, wearing uncomfortable and awkward gloves, masks and gowns.)