No. This protective action WILL be taken if a particular ONE of those two fans fails. Which one?
Any fan header (Including the CPU_FAN) can deal with only ONE fan speed signal fed to it. The signal is a series of 5 VDC pulses, 2 per revolution, that the header can count. So the Splitter supplied with the cooler system will only send to the header the speed signal of ONE fan. If you examine the Splitter's two output male connectors, only ONE of them has all 4 pins in it, and the other is missing Pin #3 so it cannot send that speed signal back. The header can then monitor for failure the one fan plugged into the Splitter output arm with ALL 4 pins.
Because your mobo has both CPU_FAN and a CPU_OPT headers, there is an UNlikely possibility. You could connect the two fans the those two headers separately without using the Splitter. Those two headers are simply mirrors of each other, so that would control both fans identically and it would work well. What SHOULD happen is the each header will receive one fan's speed signal and measure that, and be able to detect failure in either fan independently. IF a failure happened on either fan / header it should pop a warning on your screen to alert you. BUT thereafter I do NOT know what further action would be taken. On most mobos IF the failure is detected on the CPU_FAN header, in a short time it would actually shut your system down to prevent CPU overheating and damage due to NO cooling. Further it may well refuse to allow you to boot is there is NO speed signal immediately on start-up. which is what you asked about. But in your case with a failure detected on only ONE of those two headers, I do not know what action would ensue. That info is almost never provided in a mobo manual. You MIGHT be able to get that question answered by Tech Support at Gigabyte.