If anyone else wants to test it, here's what I did:
1) Go to Rigs -> Volume Pedal Settings and set location to input and to +5.0, with no volume pedal plugged in.
2) Select Lock Vol. Pedal.
3) Sort the attached profiles by gain ascending.
4) Play each profile until you hear a large gain jump.
5) Notice that the compressor is disabled on the profile where this happens.
6) Enable the compressor and notice the gain drops a large amount.
7) Set Intensity, Attack, Squash, and Volume to zero. Notice that the gain is still affected. If you set the volume higher, it still drops the gain, which is odd. If you set the mix to zero, as well, I believe it is still affecting the gain, but not to as high a degree.
8)Set Rigs -> Volume Pedal Settings and set location to input and to +-5.0, with no volume pedal plugged in.
Repeat the above tests. Now, the compressor still has the effect of dropping the gain, but it is very subtle compared to when the volume pedal at +5.0 with nothing plugged in.
I'm not sure why volume pedal settings affect the tone when no volume pedal is plugged in. I'm also not sure why a compressor would so drastically affect the gain when the settings were at zero. I'm curious to see if anyone else can reproduce that behavior. Thanks for all the help.