yes, but all the characteristics of the power amp signature were captured in the profiling process and are part of the Profile, which makes it necessary for the power amp stage to be as linear as possible to deliver the authentic sound of the amp.
Yes, those characteristics were captured in the profiling process. The caveat of the linear power amp (especially at higher volumes) is that because it is linear, it doesn't interact nor can it replicate the interaction of a tube power amp and speakers which is what the OP is lacking. The "push and pull dynamics" don't occur. Linear SS power amps into non linear guitar range speakers will always lack this interaction. It's simply the nature of the beast. Kinda like how a germanium fuzz pedal needs to be directly connected to a guitar for it to perform as intended. Put a buffer (a linear device) in between the guitar and fuzz and you lose the interaction, dynamics and the sound is changed. MOre or less the same phenomena.