Doppler distortion obviously exists. The question is one of how audible it is.

My feelings are "not very." You don't hear people who own full-range
electrostatics complaining about Doppler distortion.

Consider the following. Suppose an electrostatic speaker is reproducting 60Hz at
a peak-to-peak excursion of 0.25". That means its maximum velocity would be
around 30 inches per second. That's less than 1/4 of 1% of the speed of sound!

I really, really doubt that's audible.