After getting a LiPo and now powering-up Nova quad for the first time ... it seems like this circuit is for the Power-Board's independent, speaker-based, Low-Battery Voltage Alarm with progressive scale audio count-down (and lower lights flashing). Seems to activate around 10.6v. With quad on bench and not running motors a lot, the battery lasts quite a while.
Edit: It's about a month later now. With help from the RCGroups Forums, it seems the mystery of the Red-Wire is mostly solved. Seem this wire is either controlling the lower LED lights (soldered to bottom of ESCs) ... or at least causes them to flash during a Low-Voltage-Alarm event. In MP/Terminal - run Motor Test to see why I say that. Speaking of Motor Test, note that the testing order starts at Motor#1 and then proceeds Clockwise around the quad.
From what I can tell, there is no 12v-to-5v DC-DC converter on the ESCs to power the LEDs. I think the +5v for the LEDs might come from the Power-Board through the heavy gauge white wire on the ESC PCB Input edge. Voltage is only supplied when it deems it appropriate (see above paragraph) and that's how they light and/or flash.
Apparently, my HK LiPos are on the slow-boat-from-China. Went the LHS (HobbyTown) and picked up a Predator 11.1v 2200mah LiPo battery pack for $21. It's not the max. size or mah, but it works fine. It also had the wrong connector, so I soldered my first ever XT60. Set Soldering Station to 390c. Strip back wire insulation 1/8 inch. Pre-tin wires and don't forget heat-shrink. Use flux when soldering connector. A vice or helping-hands will come in handy.
Temporarily remove all your ESCs from the FC and reinstall DuPont one at a time. Supposedly, you can Arm when only 1 is connected. If you are getting 5v to the FC and RX (from BEC circuit) then the PowerBoard is ok. There are no active components between the ESCs and the battery's 12v.
I've since made this post with more info about power-system and ESCs. I also have a post about BEC.