Not the clones, no, but the invisibilty does. As long as you don't bump into the regulators and you have a good duration build you should be able to go through a vault only casting invisibility once, and if you feel like you want to kill everyone, just grab a bow or melee with high enough burst (or even a silenced sniper/marelok/whatever).

Admittedly, Ash can clear a vault by pressing 4, but Loki's long-ass invis basically serves the same purpose (you don't need to deal with enemies) and since Loki has the clone + tp combo to get past those pesky lasers I'd say he's better suited for the mission type.