The functionality of the theft deterrant system's horn doesn't mean anything. I have yet to see a Toyota, factory alarm which didn't have a seperate horn for the alarm system. Looking at the wiring diagrams neither the alarm horn nor the two hazard horns have a relay.
Wiring diagram for the two hazard horns:
http://www.cygnusx1.net/Supra/Librar....aspx?S=E&P=13