Yes, but it's not so easy... You have to record it because music changes from moment-to-moment. And you're probably going to have to record digitally and then the digital data won't be identical because you are sampling an analog waveform and you can't sample the exact same points on the waveform every time.
And there is always SOME analog noise which is random so it will be different every time, even with the same amp, although the noise, if you can hear it, will sound the same from the same amp.
Once you have two digital recordings you can subtract and if you get pure silence (which you can get if there's no analog involved) that proves the data is identical and the sound will be identical. But if you don't get pure silence, that can be misleading too... The difference
in the sound isn't the same as the sound
of the difference. The simplest example is a time-shift of a few milliseconds which doesn't change the sound at all. But when you subtract, you can get a difference file that's "louder" than either file alone, and you'll get comb filtering which you might recognize as related to time-shifting, but it doesn't sound like a time shift.
And if there is a small difference you may hear it clearly when listening to the difference/defect alone but it might be masked (drowned out) when listening to the "original" files.
So, it's easier and more reliable to measure known test signals, or to do
controlled blind listening tests. But even then, with measurements or blind listening tests, your hearing may be better than mine....