If the pilot experienced a medical condition that effected the command process than the lack of a current medical (if correct) may have been a contributory factor.
However, we have no idea yet what caused the accident.
There seems very little point speculating whether or not this was a factor at this stage. In fact there is nothing known at the moment to point to this even being a more likely factor in the accident than any other.
Keep to the facts and we potentially have much to learn from this sad accident, depart from the facts, and we might just as well discuss gnerally why aircraft crash.
The report that the pilot may have been inclined to push the limits could well be a factor and could be relevant. However this could also have been an isolated incident by an inexpereinced (at the time) pilot.
I am sorry this accident has occurred.