Usually the only situation where a faulty cooling pump may shut down your computer straight at boot is if your motherboard/bios is set to shut down on missing fan and the pump is somehow rigged so that the motherboard can detect the pump as a fan. Some water cooling systems also jerry-rig themselves to the cabling so that they can 'self terminate' if they detect an internal error.
If you look at the flow chart for the motherboard startup troubleshooting two issues early on relate to the cooler.
"Check if the CPU cooler is attached to the CPU securely. Is the power connector of the CPU cooler connected to the CPU_FAN header properly?"
The CPU fan must be connected and so with water cooling is this connected to the pump?
Later in the flowchart
"When the computer is turned on, is the CPU cooler running? if No -The power supply, CPU or CPU socket might fail."
It seems to me that given the tool of the manufacturers flow chart, you should at least give it a go
Edit: just to add, there are two manuals for the motherboard. One is a simple installation guide, the other which I linked to is the full manual.