It would depend entirely on the signal and output level. Probably just some theoretical scenario and not a real life one, but imagine a 20hz sine wave at 120db during an important 200hz note. Again, purely theoretical. but I'd presume some level of doppler effect.
This phenomenon is more accurately described as phase modulation which results in frequency modulation. While the acoustic phenomenon is the same - which renders this point a matter of semantics and academic perspective - this fascinating article demonstrates why using the term Doppler to describe this effect is actually incorrect.
I've committed this sin many times in the past, so I'm not being condescending; rather just sharing what I've learned about this particular subject as it relates to the type of frequency modulation to which you were referring.
Since the phase and frequency modulation effect does not exist when the woofer crosses its zero (resting) point where cone velocity is the highest, the term Doppler cannot be used to describe the phenomenon. The phase/frequency modulation actually exists at the cone excursion extremes, where cone velocity is zero (thus precluding the term Doppler to describe the effect).
The below article has the objective data supporting the claim, and Linkwitz apparently thought so much of the research that he corroborated and provided mathematical proof on his website. Far from light reading, but nevertheless fascinating if you are into the theory behind certain acoustic phenomenon like you described above.
http://sound.westhost.com/doppler.htm
