i can add to my previous comment that this applies to precision instruments where they can measure very small variations, like color analyzers (in photolabs or for calibrating a display) where high precision is required.
this would not apply to audio tube amps.
This was the case when i was in the Navy.. If any of the precision equipment that we had was ever turned off, there was an extensive start up procedure.. But that equipment was sensitive to 1/2 or 1/4 volt deviations..
I think that there will be some temperature drift with the transistors in the solid state audio amps that we have, but i think that the drift is so small that it would be inaudible.