Yes, current consumption is important. Almost all mobo fan headers can supply power at 12 VDC up to 1.0 A total current draw for all devices on that one header. OP's AIO system has one pump and one fan. These have max current ratings of 0.30 and 0.34 A respectively, total 0.64 A max. NO problem to fit within the limit of the CPU_FAN header.
One possible reason for NOT connecting both pump and rad fans in a AIO system to the CPU_FAN header is that these two devices require different power and control systems. In most AIO systems (including the one OP has) the PUMP requires power at 12 VDC at all times so that it always runs full speed, and the Rad Fan(s) require feed in the new PWM Mode system. The latter supplies a constant 12 VDC on Pin #2, and the new PWM signal on Pin #4. The PWM fan has a small chip inside to use the PWM signal to modify flow of current from that supply on Pin #2 through the motor windings to achieve speed changes. However, this all CAN be done easily if you understand the units.
The PUMP is wired just like an older 3-pin Voltage Control Fan. The ONLY way to reduce its speed is to reduce the Voltage supplied on Pin #2. When such a fan or pump is connected to a header operating in PWM Mode, it receives from Pin #2 a constant 12 VDC. It does NOT receive the PWM signal from Pin #4, and it does not have the special chip so it could not use that signal, anyway. Thus this pump or fan always runs full speed.
The RAD FAN of this system is the new 4-pin PWM design, so if it is connected to those SAME signals its gets adequate power AND its speed IS controlled by the PWM signal.
So we use this "trick" that depends on these design differences. Connect BOTH the PUMP and the RAD FAN to the same CPU_FAN header using a Splitter. As I said, the max total current fits within the header's limit. The PUMP will always run full speed as intended because the PWM system supplies 12 VDC constantly from Pin #2 and the fan cannot use the PWM signal to change its speed. The Rad Fan(s) DO have their speed controlled by the PWM signal set from that header.
When you do things this way there are THREE additiional items the require attention.
(a) The PUMP MUST be connected to the ONLY output connector on the Splitter that returns its speed to the host header. A VERY important second function of that header is to monitor the speed signal of its device for FAILURE, and the CPU_FAN header will take more-drastic corrective actions than any other mobo fan header, and do so quickly. It can shut down the entire system rapidly without waiting for the temp sensor inside the CPU to indicate rapid high tempertures. This can be done ONLY if the speed signal sent to the CPU_FAN header is the PUMP speed. In an AIO system, this is the one thing that must not fail! For a Splitter that looks like a collection of cable "arms", there will be only ONE male output connector with all FOUR pins inside, and this one WILL send its device's speed signal back to the host header. All other outputs lack Pin #3 that carries the speed signal. For other Splitter or Hub designs, the one output that sends back its speed signal is marked.
(b) The header MUST be set to PWM Mode - NOT to Voltage Control Mode (aka DC Mode), and NOT to Automatic Mode. Only PWM Mode will send out the consant 12 VDC supply and PWM signals. If you leave the CPU_FAN header in its default Automatic Mode option, at every start-up it will test the connected device's speed response to a PWM singal and discover that the PUMP does NOT reduce its speed that way, so it will change itself to Voltage Control Mode and force the PUMP to run slower!
(c) Because this method does NOT connect the RAD FAN speed signal back to the CPU_FAN header that fan's speed will never be displayed anywhere, nor can it be monitored for failure. So from time to time the USER needs to look and verify that the fan(s) are still working.
It is POSSIBLE to use a CHA_FAN or SYS_FAN header to power and control the RAD FAN(S) of an AIO system ONLY if the header has an option to allow it to use for guidance the temperature sensor inside the CPU chip. Many offer that option, but many do NOT. You should NOT try to control the RAD FAN speed according to the default temperature sensor on the MOBO.
Although you can connect a PUMP to a CHA_FAN or SYS_FAN header and set that to a fixed full speed option, I do not recommend that because such a header will NOT protect the CPU chip from rapid overheating if the pump fails and returns NO speed signal.
Mobos that have AIO_PUMP or CPU_OPT headers make alternative connections possible, too, and preferable. BUT many mobos lack those extras and require that you use only the CPU_FAN header for these functions. That appears to be OP"s situation.
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