No. Noise doesn't necessarily directly translate to distortion. That's why we have the standard THD+N, that's total harmonic distortion + noise. Now it can abberate the music but it doesn't affect THD - but can affect linear distortion. And artifacts? No, artifacts mean the component is DAMAGED or has a severely bad connection on the digital side. You can't get artifacts in normal playback aside from the sound of clicks and pops in vinyl. In order for it to come through the speakers from the power side you'd need something severe like a lightening strike or transformer popping somewhere not far off.
And as far as experiencing music as pure as possible... That's a load of shit given that the best measuring stuff is nearly completely hated on this forum. So clearly what makes something sound good is not as you say, or what you say...
Incorrect, see above. These are unrelated factors. To the same effect that you can have an amplifier that has a sizzle with your head next to the speaker but gives you all the qualities you list in spades, and even well over other amplifiers that have no sizzle.
But Ron does bring up a good point, does the noise matter? Well it really depends on what kind and where it is/comes from. Slightly noisy tubes and transistors clearly don't seem to be a problem at all except for with overly paranoid electrical engineers that can stand the idea of it, despite having no evidence what so ever that there is an audible issue. But the moment you start connecting kitty litter boxes as antennas the parasitic or other effects cause desirable or undesirable results (depends who you ask). Consider the rebadged Marantz CD players being sold for tens of thousands of dollars with only the addition of a noisy output... or the super high end amps that have a dirty transistor at the input but get awards and praise all day. Clearly noise is a double edged sword, usable for good by some and not others, and never universally binary. Sometimes it makes things awful, other times it's a byproduct of other superior qualities. There's no much of a reason to develop philosophy on it, just listen to the gear you like.