This was the first PC I built so I only have what I bought to put this together.
I put the CPU fan in BIOS as ignoring to avoid the CPU Fan Error and left it a few hours so it was cold to avoid the CPU Temp Error and it booted up. I ran Open Hardware Monitor and Corsair Link side by side and took a screen grab every minute till it shut down.
https://postimg.cc/gallery/2tfszpc0g/
C-Link read the temps as about 10C higher than OHM, the temps out of OHM looked about the same as the temps in BIOS. C-Link also recorded the Pump as working at about 2440 rpm up until the PC shut down.
By Stock Cooler you mean one of the metal blocks cut into fins with fans mounted on them? I could pick up just to test it out I guess, they seem to be cheap. I'm a bit less certain not C-Link is claiming the pump is working.