There are THREE factors to consider in this question because the headers have at least THREE important functions and some limits.
1. Almost ALL mobo fan headers are designed for THREE functions equally important:
(a) provide POWER to its "fan" or whatever is plugged in. Max VOLTAGE is 12 VDC, max AMPS commonly is 1.0 A; some (see your mobo manual) provide more.
(b) CONTROL the speed of the fan. Actually what it really is doing is to control the TEMPERATURE as measured by a sensor associated with the hot item it is cooling. WHICH sensor is used is important! There is always one inside the CPU chip (and sometimes others in the CPU socket on the mobo) used to guide CPU cooling. There is a second on the mobo that the maker judges is a good representation of the cooling needs of ALL of the important mobo heat sources. There MAY be more associated with particular mobo components, and these can be used IF you are dedicating a fan to cool that item. The automatic control system MANIPULATES the fan speed to move enough air to keep the sensor temp on target. It does NOT care what speed that requires - it changes the speed control signal to the fan to whatever it takes to get that sensor temp right.
(c) Monitor the speed signal of the connected device for NO signal (in a few cases, a signal of speed below a min) which would indicate FAILURE of that source of cooling. Any failure should (you can disable this on some fan headers) pop up on your screen a warning message so you know of the problem. On most mobos if failure is detected at the CPU_FAN header it will take much more aggressive action to prevent permanent damage to your valuable CPU chip by lack of cooling. Usually this means shutting your system down completely in a short time without even waiting for the sensor inside the CPU chip to show excess temperature. Such headers often will NOT allow you to boot up if it gets no speed signal right away at that header when attempting to start up.
ALL of these factors are important when using AIO cooling systems. Consider what is REQUIRED from such systems.
POWER is needed by both the pump and the rad fans. MOST systems are designed to have the PUMP run full speed all the time, so it requires the full 12 VDC always. The RAD FANS need this power but also speed control.
CONTROL of cooling should NOT be done by having BOTH the pump and the rad fans change their speeds. The impact of changes of each of these units has a different magnitude and a different time delay, so IF you have them both altered by the sensor temp, one lags behind the other then catches up and overshoots, and the two items "chase" each other constantly. The common way to solve that is to have the PUMP run at a constant full speed, and let ALL control of CPU temp be done by varying the speed of the RAD FANS. There are SOME systems with provisions to let you manually set the pump speed to a lower value but still constant, and that works fine but MAY limit max cooling at high workloads. There are some systems that base their control on a temp sensor in the liquid flow loop rather than on the one inside the CPU chip. However, you can NOT use any temerature sensor on the mobo to guide this CPU cooling system. For that reason almost all CPU_FAN headers can use ONLY the CPU chip sensor for guidance and give you no choice on that.
Regarding FAILURE detection, the most important item in your AIO system is the PUMP. If it fails there is NO movement of heat from CPU to Rad and the CPU will overheat VERY quickly. On the other hand, if the pump IS working and one or even ALL RAD FANS fail, the CPU temperature will rise slowly and other protection systems based on that temp sensor will take over and slow the processor to reduce workload, or eventually shut down in extreme cases. So, if you MUST choose, ensure that the PUMP is connected to the CPU_FAN header for proper FAILURE detection. Now, many mobos have also a CPU_OPT header which merely is a copy of the CPU_FAN header. Some aslo have dedicated AIO_PUMP headers, OR a header that can be configured to do that job OR behave like a normal case vent fan header. One would hope that each of these alternatives also DOES do the failure detection function the same intense way, but I almost never see any assurance of that in a mobo manual.
Beyond cooling the CPU, the mobo has SYS_FAN or CHA_FAN headers intended for general case cooling. These cool mobo components, and supply air flow through the case for use by a CPU air cooler and by any graphics card added in the system. MOST of these headers have an option to select whether it uses for guidance the temp sensor inside the CPU chip, the one on the mobo, or any special mobo temp sensor. The option to use the CPU internal sensor is useful IF you need to connect to it a fan that is part of the CPU cooling systen - for example, rad fans. But I would NOT use these for the PUMP because they do NOT do the intense CPU protection actions on FAILURE detection.
If you have enough of the right headers to use (see last paragraph below) you can split up the pump and rad fans. But in situations where you have limited headers to use, sometimes you need to connect BOTH the PUMP and the RAD FANS to the CPU_FAN header using a SPLITTER. IF this is done correctly it CAN provide all these items need. It can provide constant 12 VDC power to the PUMP, it can monirtor the PUMP speed for FAILURE, and it can CONTROL the speed of the rad fans. Doing all that uses a "trick" of fan design. PUMPS designed to run full speed all are wired just like older 3-pin fans on which the ONLY way to reduce their speed is to reduce the VOLTAGE supplied from Pin #2. Any fan OR pump designed this way will always run full speed when plugged into a header that is using instead the newer 4-pin PWM fan control system. In that newer system the power on Pin #2 is always the full 12 VDC, and the new PWM signal on Pin #4 is used by fans of that new design to control the fan speed. So IF the pump is like this - a 3-pin design - AND the RAD FANS are the new 4-pin PWM type (and this is almost always the combination in a AIO system) then connecting all of those to the CPU_FAN header and ensuring that it is configured in BIOS Setup to use the 4-pin PWM MODE of control will provide the correct power AND speed control for them all.
BEWARE of one important item here. MANY such CPU_FAN headers offer you a choice of MODE that includes Voltage Control Mode (aka DC Mode), PWM Mode, and AUTOMATIC Mode. In Automatic, the header will try to start in PWM Mode, testing whether that is able to reduce the "fan's" speed. If it does NOT (which would happen with the PUMP), it concludes the "fan" is the old type and changes to Voltage Control Mode so it CAN force the "fan" to slow down. That is exactly what we no NOT want for the PUMP! So you MUST set it to PWM Mode to guarantee the power from Pin #2 will stay at 12 VDC.
Others have mantioned above the imprtance of the AMP limit on the CPU_FAN header. As I said, most are limited to1.0 A max load, although some are higher. This is important when you use a SPLITTER to connect both the pump and all your rad fans to one header like CPU_FAN. First you need to get the specs for the max amps required for EACH of the fans and for the PUMP. In most cases these will be from 0.10 to 0.25 A each, so the total is under 1.0 A. BUT that is NOT guaranteed, so you MUST get the specs for YOUR system and do the calculation.
IF you are using a SPLITTER to connect both pump and fans to the CPU_FAN header, there is an IMPORTANT detail to do. Fans and pumps send their speed signal (consists of 2 pulses per revolution) back to the host header on Pin #3 for counting to calculate speed. The header can deal with such signals from only ONE device, so a SPLITTER or a HUB will send back the speed signal of only ONE of its devices and ignore all the others. You will never see the speeds of the "others" anywhere. In common Splitters that look like a collection of cable "arms", only one of the male output connectors will have all FOUR pins. All the others will be missing Pin #3. ONLY the one with FOUR pins can send its speed back. That signal is how the header can detect FAILURE! So in an AIO system, you MUST plug the PUMP into the one connetor with all four pins! In other Splitter designs like circuit borads or boxes with recessed sockets, ONE output will be marked as the only one to send back speed. Then realize that failure of the FANS on the other outputs can NOT ne detected. So from time to time YOU should look and verify that all the Rad Fans are still working.
One great way to avoid overloading the Amps on a header is to split up the load. If at all possible, depending on what headers your mobo has, the prefrerred arrangement would be one of these:
1. PUMP on CPU_FAN, RAD FANS on CPU_OPT
2. PUMP on AIO_PUMP, RAD FANS on CPU_FAN
3. PUMP on CPU_FAN, RAD FANS on SYS_FAN IF you can set that header to use the temp sensor in the CPU chip, and NOT the one on the mobo.
4. PUMP on a SYS_FAN / PUMP header that CAN be configured for PUMP operation which WILL feed it full power always, PLUS we hope it will take strong action IF the PUMP fails; RAD FANS on the CPU_FAN header.