True, good point, Karadjgne, I always advise people NOT to use those LNA's unless they are connecting to a fixed uncontrolled 12 VDC supply (like, from the PSU via Molex). But still, the normal sequence I am used to is that, at initial start-up, a fan header sends out full 12 VDC to ensure the fan does start, then throttles that down either by reducing voltage or sending a low-speed PWM signal. Thereafter if it gets a zero-speed signal it first attempts a re-start with a full-speed signal or Voltage. If that fails to get a good speed signal it issues its on-screen warning of fan failure. Now, if OP's connection yields NO speed signal, what I call "normal" would result in the fan starting up at full speed, then maybe slowing down and maybe stalling, followed by the failed fan warning. That is, if that warning has not been disabled in BIOS Setup. But again, we do not know whether or not OP observed a sequence like that - no details.
Worst case (possibly) would happen if OP used BOTH of the two LNA's supplied by Noctua. The combo certainly could reduce the fan voltage to well below even 5 VDC, very likely to fail to start up the motor at all.