No they don't go "through that switch."
Here is how a 4 way flasher switch works in pre--"on the column" switches
First of course you have two flashers, one for 4 way (powered at all times) and one for turn (powered through key switch
When the turn signal switch is centered, the brake lamps are connected together by that switch, and connected to the brake light wire going to the brake light switch. this of course is so that when you tromp on the pedal, power goes through the TS switch and is routed to both brake lamps
That is ONE external wire...........the brake light power wire to the TS switch
The left front and right front signal lamps are separately fed to the TS switch AND THEY BRANCH OFF and feed off to the dash indicators and the fender indicators "if equipped."
So that is two more wires
HAZARD SWITCH. The hazard switch up before the switch was incorporated into the column is a 4 terminal switch, and when off, all of the terminals are connected. One goes to hazard flasher output, one to left front signal lamp, one to right front lamp, and the remaining ties in to the brake switch wire previously mentiond
When you engage the hazard switch, ALL FOUR terminals are connected together. This feeds the flasher output to the brake switch wire and on to the two rear signal lamps, and to the left front and the right front signal lamps, causing all four to flash
AGAIN, the dash (and fender) indicators ARE SIMPLY branched off of the left front and right front wires so they flash as well