It'll really depend on the rest of your setup and the quality of your PSU. A Skylake CPU (~100W) + 2x 1080 turbos (360W) and the balance of your rig (call it 100W) is right on the cusp of a 600W PSU. If it's a quality 600W PSU, it should work, but wouldn't be recommended.
600W, even from a quality PSU is likely a little low though.
I assume, considering you only mention "600W PSU" that it's probably not the best quality.