It may be location dependant, but IMHO any corpse in a morgue would be full of preserving chemicals to ensure it'd be "presentable" for the funeral, and thus inedible.
Morgues absolutely do not embalm, they refrigerate. A body in a morgue is either unidentified, awaiting autopsy/examination, or yet to be claimed. None of those categories permit embalming, and in any case, morgues are not funeral homes.