Does the FAA generally consider a door opening in an unpressurized cabin during flight to be an emergency? Sometimes doors pop open on older training aircraft during flight.  

I've read some indications from poorly-documented sources suggesting that this is considered an emergency, but it doesn't appear to be addressed in any flight manuals, the AIM, or the FARs.

Is there any publication from the FAA that indicates a stance on the issue as it pertains to it being considered an emergency or not?
A door popping open is not an emergency in itself, it has to cause a threat to the safety of the flight or those on the ground to be an emergency. I've had doors pop open in a light aircraft in flight and it has been a non-event every time, I didn't mention it to ATC as there was no reason to, I just told maintenance once I was on the ground. I've never seen a FAA or other country authority publication saying it was an emergency. 

Regs generally don't get that specific, what is life threatening on one airplane may be a non-event in another. The POH and airplane specific training is typically where emergency events are specified.