First, it would be important to look at the diet in Rome (understanding that Rome's history lasted a millennium and while many things changed, including medical practices, diet would have remained relatively unchanged). Grain and cereal was a large part of the diet and as a consequence so was fiber. Appendicitis is caused by the blockage of the appendix, often by stool (or in rare cases any inflammation such as cancer). Because of their high-fiber diet it would be very unlikely that many people developed appendicitis.

That being said, surgery was rarely practiced at all during the time. While medical practices did certainly advance throughout Rome's millennium. For most of the Republican period (~510 - 27 B.C.) the Hippocratic corpus is our most useful source (see the Hippocratic Oath in which it states "I will not use the knife, not even on sufferers from stone, but will withdraw in favor of such men as are engaged in this work"). During the Empire Galen tends to be our most useful source. While surgery and dissections became slightly more practiced (albeit more on animals than humans), the practice as a whole was comparatively non-existent.

TL;DR as unlikely as it would have been to develop appendicitis, if the miracle occurred, surgery would not be an option and the disease would likely be a death sentence.