Unlike the fueler, the door had a direct role in the event since it prevented the captain from getting access to the flight deck in a pretty dire situation where his presence could resulted in a different outcome (for the better or worse).
I have the opinion that the presence of the captain could have acted as a "limiter" to the actions that took place so yes, that door had its impact on the event.
It is not a cause, obviously but it is totally clear to me that the outcome would have changed in one way or another *if* the captain had been able to open the door. It would be either for the worse (the F/O disconnecting the A/P and initiating a steeper descent) or better (the ability to take the control back and level off, thus preventing the crash).