Since they haven't located separate debris suggesting elevator detachment/damage it suggests to me that a c of g issue alone is unlikely.
If part of the elevator (or tail) departed at high altitude, it could potentially be many miles from the (main) crash site. Given the remoteness of that whole area, such relatively small part(s) might not be located for months or even years.
I'd think that since they were able make a Mayday call, crew incapacitation would be unlikely, but as pattern_is_full noted, never 'assume' anything.