VIBRATION: Spectrum & Timbre

 Answer 

Yes, they do sound the same for listeners!
The micro variations in the actual amplitudes are not significant for the auditory system. They are not "differences that make a difference," in the words of Gregory Bateson. And besides, they will differ with the next note played similarly.

The oft-told anecdote for this example is that at first, listeners could tell the difference: the "real" sounds had tape hiss, and the synthetic ones didn't! I guess they had to add some hiss to the digital ones to make them sound "real"!