Yeah, tried that. There are no good reasons to do this. What exactly is the goal?
It generally feels like it just starts loosing some detail or maybe gets rolled off even further.
For me one of the motivations was to try and achieve tube distortion for my electric guitar but I believe I did not push the "preamp" amp far enough to make the "power amp" amp start clipping the sound!
Note, that this was using Garage1217 amplifiers which feature a design that both has tube-driven variable output gain and variable input gain by swapping optional gain modules.
I might get a 12ax7 tube and try again one day along with the highest gain input module...