If you had a serious illness, would you continue to serve in some capacity?

Yes, while recovering from Stage IV neck cancer (thanks to the great medical staff at Tripler AMC) a compassionate CG medical director allowed me to remain in service so I could continue accessing support services. Longest year of my life but it was also the best year as I continued my service. 

Given the fact that I already avoid medical at all costs regardless of how I usually feel, I would guess that any serious disease would probably be found in the autopsy they do after I mysteriously collapse dead while still on the job.

I mean, it would depend on how debilitating the disease is. If it's something that is killing me but not affecting my job performance than I would probably finish this enlistment or at least try to. If it was debilitating then I guess I would take my medical retirement and bounce. I do have things I want to do yet so I wouldn't want to miss out on those opportunities completely if I didn't have to.