100% correct, about 95% of the tone comes from the fingers. Vai would still sound like Vai playing through a Epiphone and 10 watt practice amp, the gear just provides the icing on the cake.
Re the 81/85 combo, I have it on two guitars - a Dean MAB-1 and an Ibanez Prestige. Very nice set, high output which is good for lead. Not very 'heavy' for rhythm though - to get major power out of them you would probably have to go through a tube amp with monster distortion pushing at high volumes. They do help generate nice distorted tones though, good crunch but it's not very thick and seems to lack bottom end - more suitable for lead IMO. I have heard of guys swapping the 85 to the bridge as it is way boomier - havent tried it myself though. The above link gives the advice re 18v - seems to be for powering two off the one.