In my opinion the gear Vai is using makes a huge impact in the resulting tone.
But he himself said once that the tone ultimately comes from your fingers… how you fret a note, apply vibrato, attack the string, etc.

So, having the same gear is gonna get you close to his tone; but you gotta have the chops as well.

Dimitar Nalbantov is a great player, he has the right gear and is very influenced by Satch and Vai.

I haven’t got a chance to try one of those suckers, but I’m pretty sure they produce a variety of tones.