You can disable the cpu fan fail warning in the bios. The only way you're going to get motherboard monitoring of the cpu fan is if it's connected to the CPU_FAN header on the motherboard, not a fan controller.
You may be able to adjust the settings in the bios, for cpu fan speed control. Asus boards have what they call Q-fan, you can set the cpu fan speed to silent, normal, or performance. Other brands of retail boards have something similar.
The gigabyte controller was probably a single in-line controller, which draws it's power from the motherboard header, but, since it's in-line, it can slow it down and speed it up.
Something like the Zalman Fan Mate 2 will do that, but not in conjunction with the 4 channel controller pictured above, it'll do it all by itself.
Newegg.com - ZALMAN FAN MATE 2 Fan Controller