I have never heard anybody ask if something is a "patient experience" rather if it is a "clinical experience" and working for the M.E. is definitely a clinical experience, albeit a non-traditional one.
While it seems to me like many people here, and even you yourself, aren't identifying this as clinical because you cannot help the "patients" themselves, the M.E. provides a great deal of extremely important information to the family and loved ones and I think you'd be undervaluing it if you don't think of it as "clinical." It shares much in common with living patient care.
Commonly physicians allow families of terminal patients to find emotional closure by helping them to prepare for the impending death and ensuring that the death is as comfortable as possible...of course we all prefer to be able to find problems and fix them before a patient dies, but sometimes, it just can't be done. Then the M.E. is very important to the family, friends, and loved ones to provide that same kind of closure. While the M.E. certainly doesn't engage the family in the same way, it is his/her findings that are often able to provide the most positive aspects of the death--hopefully that the decedent passed peacefully, without pain, or quickly, and in the most tragic incidents by providing the scientific basis upon which a criminal will hopefully be convicted, etc.
The M.E. is the person who:
-keeps loved ones from endlessly wondering "why?"
-often knows the statistics to help the family find communion in their experience (i.e. that this was commonly an unpreventable means of death and impacts X families each year)
-has the incredible responsibility of determining the less obvious causes of death of deceased newborns/still-borns--a particularly common but gut wrenching occurrence for new parents that is utterly difficult to grasp.
Most of the highly specialized physicians I work with do specialized consulting as M.E.'s in their area of expertise. This is not an overlooked need in the medical field. There are at least two med schools I know of that offer rotations through the coroner's office w/ the ME.
You can express a love for a field, but profess your openness to other fields...it is commonly believed you are too inexperienced to know any better as an applicant! That's the purpose of rotations.