Though in contrast, guitar amplifiers with vacuum tubes in the power amplifier stage does have a huge difference in sound AFTER the tubes are warmed up after a few minutes.
In my limited experience with guitar amplifiers, a heavily distorted solid state transistor amplifier sounded the same the moment it is turned on, regardless of what the volume was set to at the power on.
I don't know if there's any way to convince myself of the opposite, for heavily driven...