Live wire spliced in a switch to provide power to other parts of the room!
Your analysis of the current situation is correct and quite normal. The fact that this type of switch allows two wires to be attached under the switch makes it that much easier to do, as opposed to hacks (MPO) such as one wire under the screw and one in the back-stab.
Yes, it is perfectly fine to have a pigtail to the switch and connect the three wires with a wirenut.