Here is exactly what you wrote: "So if anything, having been sick will make Chuck Amato a better football coach."
There is little doubt spending some time in a hospital bed might change one's perspective on life and maybe help turn that individual into a better person, but will it make that individual a better (or worse, or no different) doctor, coach, accountant, or garbage collector? In Chuck's case we will be able to answer this only after we see how he does post illness. If it were the case that surviving such an illness did guarantee improved coaching, it would definitely be an SEC team that conducted the clinic.