You’re absolutely correct wrt the Doppler effect, but note: in both the case for light and say a siren, the speed of the traveling wave is constant. Therefore if the wavelength is changed due to movement, the frequency must change inversely. You’d still hear a Doppler effect on Mars if something were moving quickly, but that isn’t the case so far here.
For helium (or sulfur hexafluoride, the one that makes your voice sound super low), that does indeed affect the frequencies your vocal box generates, per the sound wave lengths you can generate being held constant (your vocal box doesn’t change in size depending on the fluid you’ve inhaled).
I should amend my previous comment: it depends on the source of sound. If the source depends on resonance of a medium (e.g. a voice box or acoustic guitar), it would theoretically sound higher, though your high-freq dropoff would still be significant. If the source is solely based on it’s own vibrational frequency (e.g. a tuning fork), no change in pitch but the high-freq dropoff still holds.
It has also been many years since I was in any physics classes, so grain of salt is encouraged. I think the best solution here is to send someone to Mars and test it out.
