I just did this (added the turn signal with headlights), but was planning on still running the original signals as well. It might be a problem with the headlights that I bought, but when I hooked it up (properly too I might add) I ended up blowing a circuit in the lights, and the main halo white LED's wouldn't work properly, so the turn signal (headlight) was amber and not white.
I duplicated this in the other headlight. Low beam, fine. High beam fine. Blinker, fine. Then any low or high beam has the halo lit amber. So something in the way the HMMWV blinks blew out something in my headlight. I was able to snip the Amber wire, and it did work properly (white halo on when lights on), but don't really trust it now (and a capacitor blew in the other one) so they are now in the trash.
So might have been the crappy ones I got, but fair warning. I was considering just buying another pair and not hooking up the blinker, but am a little gunshy on spending the money again.
Good luck! Post results and if you can, the exact model and where you bought them. I think others are considering this. So far I have only seen one type recommended and it didn't have the blinker, and he didn't hook up the DRL (daylight running lights).