Anything is possible, but I would first look for leaks as BMWFatherFigure suggested. The procedure for checking the o2 sensors is on the link. For leaks, generally speaking, an exhaust leak will at least make some additional noise and is best diagnosed on a rack with a funnel type mechanics stethoscope-- if not apparent enough to be clear from where the leak originates. That same tool will be useful for finding any future vacuum leaks as well. Where are the tail pipes on this one? Factory tucked under the rear bumper cover, or does it have tips showing. I ask because if the trunk ventilation flaps are malfunctioning, exhaust gas is basically sucked into the car. Is the HVAC control set to recirc or fresh air when the smell gets worse?
It's not what you buy, it's what you build- Unknown
EN90283 - Stabled for HG repair
DH06247 - Running like a champ