You could say that we put your question to the test every time we speak.

Remember that the atmosphere we breathe is itself a mix of gases of different densities. However, When we speak in air, we do not get two tones emerging from our mouths, one of them appropriate to oxygen and the other to nitrogen.

The fact is that the frequency of vibration of our vocal chords is affected by the atmosphere' s bulk characteristics, not the characteristics of the individual gases independently.

I am not aware of anyone trying it with mixes of gases as widely separated in density as helium and sulphur hexafluoride, but people are breathing a mixture of helium and oxygen produce notes roughly consistent with the density of the mix of gases that they breathe.

So, it is a pretty question, but a pedestrian answer. Sorry about that!

Cheers,

Jon