He'd have to be reeeeal quick, too. Because by the time he tries to figure out which is which, the other amp will be allready "burned in"
EDIT:mbd2884@ I personally find cable burn in sort of hard to believe in but somehow, I still wouldn't dismiss the possibility that a virgin cable will perform kinda funny the first time he (or she) meets electricity
Theres a difference between burn in and perceivable change if you ask me. Does burn in exist? Yes, things change though usually much faster than what people think, a frequency range of a headphone or speaker could settle.
However does a peice of equipment change over 50-300 hours and cause your "harsh" sound to turn "liquid" or make any other specific aspects of the sound change enough that any human would notice? Heck no.
People give themselves far too much credit, the human ear simply is not even remotely that sensitive.
As far as solid state components breaking in, again that doesnt exist. Not on a perceivable level.
This is no different than someone saying they can hear the difference between a cable that uses some silver vs one that uses a solid copper core. The same goes for silver component wiring or silver solder. People will hear whatever they want to hear, whether it exists or not. And this is often related to what they spent for said component they hear changing as well. How many people who've spent hundreds or thousands for their components will admit they're a waste of money?
The more likely rational behind burn in is that people are re-assuring themselves that they have made the right decision, they become accustomed to the sound, and learn to like it. Volume changes, pad wear, driver positioning etc.. all play an important part as well and all will affect the sound quite significantly explaining perfectly any actual changes that people might hear.