Does the FAA generally consider a door opening in an unpressurized cabin during flight to be an emergency?
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.