In a way yes....
And there would be this nice big data trail for law enforcement to follow.
"Hey look, just before this guy got geeked, he transferred all his money to this account! Lets go ask/find this guy as he was the last person to see him."
Remember, in the digital age that is SR, every inch of the world worth living in is recorded, digitized, analized, and surveyed. Thanks to both drones, cameras, and RFID readers and scanners. (This is what makes technos/deckers such valuable team members! They can obfuscate or even remove this data trail from the matrix, thus keeping the 600 vending machines, light standards, drones, and stores you past from pointing an arrow to where you went!)
So unless Mr. Mage kept his hunting to the slums, he's GOING TO GET CAUGHT! (Just a question of when... not IF). And if he's hunting in the slums, he's not getting much.... after all, just how much money does people on a low lifestyle have?? These people fan barely afford flavouring for their 3 soy meals a day!
So that means hunting in a better part of town.... which means security... the higher the zone, the more intusive the security....
So yea, let the mage do it... a couple of times, then 'throw the book at him' litterally. Being a mind raping thief murderer is going to bring the heat like no ones business cause he's hitting just about every trope main stream society hates and fears...
Magic
Mind raping
Murder
Thieft
They'll come at him using 'standard Lone Star proceedures' no matter what corp they are...
(In case you don't know what standard LSP is, it goes: <Blam! Blam! Blam!> "Freeze! You're under arrest!")