The thing is, if you listen to the original 'recorded' Vai tones, then listen to the same songs on one live show, then another live show, the tones are all different...his own signature tones are inconsistent...what's consistent is the way he plays the actual solo.
It is absolutely true that when we serach for an artist sound or a song tone, we find different sounds in all the different verison studio and various Live, but it is also true that the main characteristics/parameter/effects/settings of such sound remains constant trought the various version, than the artist has in his hand big part of the tone obviously.
I think we overcomplicate "signature' tones, the signature is in the way you play it, not the actual tone.
... let me describe my personal conclusion on this topic: that every signature tones is a mix of hands/way of playing/guitar used/amp+effects. All is needed in different percentage for the scope, and only working on all these factors together we can achieve the best results.
How much is important one vs another??? Well, I believe it depends, song by song, on how much is complex the effect chain used and all the rest...
What is amazing now in 2014 is that finally with the Kemper we can switch just a button and pass from Vai to Gilmour to Knopfler to Moore etc etc, and all sounds great and absolutely realistic