If you can prove this to me then you will have disproven my
hypothesis!

Have you done any of the testing suggested here yet? I would like to see
the results.

I know you like the Lame encoder (notlame uses the Lame encoding engine),
so you should be comfortable with the command line Lame encoder wich allows
you to specify the ATH threshold.

Download an app that can create a test tone at a specified amplitude.
Create a wav file with a test tone at a very low amplitude. Encode this
with a manually specified ATH (so you know for certain what it is). If the
test tone disappears your hypothesis is correct, if it doesn't disappear
your hypothesis is incorrect. Try this with different amplitudes and
settings if you feel uncertain of exactly what the parameters in the apps
really does.

And once you've done this, post the results here so we all may know the
answer.

If this shows your hypothesis to be correct, I would suggest that
using Lame and manually setting the ATH to a lower value would be a better
way to reach your stated goals than to compress the audio before encoding.

Regards
/Jonas