Wow, I think this is too risky.
Atonality means no tonal center, but not lack of harmony. There is harmony in every kind of music. Other thing is that the harmony you hear is not tonal and hierarchical according to classic standards.
In the Gymnopédies there are tonic centers. Again they are established in different ways. Most parts of Gymnopedies are modal. Modal music have also "centers", call them tonic center or whatever, but the music runs around the center.
Atonality and politonality is not the same. In bitonality you have TWO tonal centers, and in true bitonality you need full development of each tonality with dominants and tonics. In politonality, it's the same but with more tonalities. When there are no tonal centers at all, you have atonality. It was the progressive "obsession" of those composers, first Schönberg was not convinced of free atonality because it could have "hidden" tonal centers, and he developed atonal dodecaphonism. Serialism was a step further.
What happens in Mars is not politonality. For that, tonalities must happen simultaneously, not one after the other. I think Holst used bitonality here in some parts with centers on G and C#).
This piece by Ives is truly polytonal: