I'm not sure I've ever witnessed anyone asking to sound like a guitar rig, they always say they want to sound like a specific player.Hex-a-pickup.
My mind separates what the artist does, his styling and articulations, from the gear. At some level the artist is an individual , but the equipment is also iconic.
If you are separating the gear from the artist, and the artist is the one with the fingers, then you are not answering the question that was asked.
Will a specific Les Paul plugged into a specific Marshall sound the same when when played by multiple robots that are calibrated exactly the same, yes.
Will that same setup sound exactly the same when SRV, Paul Gilbert, Chet Atkins and Ace Frehley play it, no.