In the 3808 you can actually transfer the results Audyssey finds to the Manual EQ. Well, sort of... The Audyssey filters use several hundred coefficients to model the measured response and create an inverse filter. The Manual EQ is simply a parametric equalizer with 9 bands. It works only in the frequency domain and does no time domain correction. So the "transfer" of hundreds of points to 9 bands is not exactly ideal, but a good starting point if you want to play with it. Of course, Audyssey is turned off when you switch to manual so they don't work at the same time.
Also, to answer your other question: every internal setting of the receiver is ignored when you run the calibration. This includes levels, delays, crossovers, manual EQ, tone controls.