That'd create a higher load on the circuit than intended if operating the flashers and third function. Wires included from WR Long were 12ga, most of the wires in my fuse block are smaller 14ga. My 3rd function came with a 10A fuse, and if I'm not mistaken, that's the size fuse already on the hazard circuit. Operating both, that could easily pop the fuse or get a wire hot.
I won't double up on an existing circuit. I prefer adding my own power lead rather than taking a chance on overloading the OEM systems. The only time I tap into the manufacturer's wiring is if I need key-on power, and then I only use their wiring to trip a relay and still bring my own power to the device.