most motherboards don't boot if you don't have an operational fan connected to the CPU fan header.
In my experience, Gigabyte boards are the least fussy when it comes to using fan headers.
With Asus boards, you should be able to disable the CPU fan alarm in the UEFI, although I didn't have any success doing this with my P8Z68-V -- the CPU fan alarm still pops up and prevents the system from booting.
To get around this, I simply connected one fan to the CPU fan header, with a resistor to lower the fan speed. And then used the CHA_FAN headers to control the other fans. With Asus boards, the CPU fan header can only control 4-pin PWM fans, while the other headers can control both 3-pin voltage and 4-pin PWM fans.